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Comparison of mass diagram and linear programming methods of mass allocation in forest road design Haudenschild, Urs Emanuel 1970

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COMPARISON OF MASS DIAGRAM AND LINEAR PROGRAMMING METHODS OF MASS ALLOCATION IN FOREST ROAD DESIGN by URS EMANUEL HAUDENSCHILD D i p l . For. Eng., 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY in the Faculty of Forestry We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1970 In presenting t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I furt h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Depart-ment or by h i s representatives. It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Faculty of Forestry The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date: December, 1970 ABSTRACT Supervisors: Professors L. Adamovich and G. G. Young A c c e s s i b i l i t y of the forest i s a basic requirement f o r a commercially managed f o r e s t . Logging in B r i t i s h Columbia often i s c a r r i e d out in remote areas where log transportation i s p r i m a r i l y by truck hauling on forest roads. Forest road construction and p a r t i c u l a r l y earth moving are s i g n i f i c a n t elements in the t o t a l cost of forest products. Proper choice of road design elements w i l l determine the optimum economy of any forest road. The d e r i v a t i o n of road design elements i s shown in d e t a i l as an introduction to the earth a l l o c a t i o n problem. Minimization of costs of main forest access roads i s studied in t h i s t h e s i s and alternate methods of mass a l l o c a t i o n are pre-sented. A semi-graphical method of mass a l l o c a t i o n (mass diagram) i s compared with a method employing the e l e c t r o n i c computer and the t o o l s of operations research ( l i n e a r programming). The theory of l i n e a r programming (LP) i s shown as the o p t i -mization technique used for minimizing the earth moving costs. The LP assumptions and l i m i t a t i o n s are discussed. The two methods were tested on the forest main haul road C in the U n i v e r s i t y of B r i t i s h Columbia Research Forest. Calculations of volume d i s t r i b u t i o n and the required intermediate c a l c u l a t i o n s are c a r r i e d out with an e l e c t r o n i c computer for comparison with t r a d i t i o n a l methods. The mass diagram method might be used f o r a long time due to i t s s i m p l i c i t y , whilst LP provides a more precise s o l u t i o n . The costs of earthmoving and planning are $84.00 or 0.6% of the t o t a l earthwork and planning costs l e s s by using LP rather than the mass diagram in the example c a l c u l a t e d . The use of dynamic programming (DP) to determine the optimum road lay-out i s suggested as a topic f o r further research, a prelim-inary step f o r optimization in mass a l l o c a t i o n . ACKNOWLEDGEMENT T h e a u t h o r w o u l d l i k e t o e x p r e s s h i s t h a n k s t o A s s o c i a t e P r o f e s s o r L . A d a m o v i c h a n d A s s i s t a n t P r o f e s s o r G . G . Y o u n g f o r t h e i r g u i d a n c e , a d v i c e a n d c r i t i c a l r e v i e w o f t h i s t h e s i s . A s s o c i a t e P r o f e s s o r A d a m o v i c h c r e a t e d i n t e r e s t i n t h e t o p i c w h i l e A s s i s t a n t P r o f e s s o r Y o u n g h e l p e d i n t h e p r o p e r u s e o f t h e o p t i m i z a t i o n t e c h n i q u e . M i s t e r H . W a e l t i , M a n a g e r , F o r e s t E n g i n e e r i n g D i v i s i o n o f t h e B r i t i s h C o l u m b i a F o r e s t S e r v i c e m a d e a v a i l a b l e t h e c o m p u t e r p r o g r a m s f o r v o l u m e c a l c u l a t i o n s . A t t e n d a n c e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a w a s p o s s i b l e w i t h f i n a n c i a l a s s i s t a n c e f r o m t h e F a c u l t y o f F o r e s t r y i n t h e f o r m o f T e a c h i n g A s s i s t a n t s h i p s . ABSTRACT I ACKNOWLEDGEMENT i i i TABLE OF CONTENTS i v LIST OF FIGURES v i i LIST OF APPENDICES v i i i I. INTRODUCTION 1 I I . GEOMETRIC ROAD DESIGN ELEMENTS 3 FOREST MAIN HAUL ROADS 3 LAND SERVICE 4 ECONOMIC OBJECTIVE 4 ENGINEERING CHARACTERISTICS OF MAIN FOREST HAUL ROADS 5 T r a f f i c Flow and Density 5 Speed 6 Weight of Vehicles 6 OPTIMUM ROAD STANDARDS 7 Selection of Design Elements 8 Horizontal Alignment 8 Superelevation i n Curves 9 Side F r i c t i o n Factor 9 Minimum Radius Due to Design Speed-Background theory 10 Ca l c u l a t i o n of the Side F r i c t i o n Factor f o r Forest Roads 14 Maximum Degree of Curvature 15 Curve Widening 16 V e r t i c a l Alignment . 20 Grades 20 Maximum Adverse Grade 21 Ve l o c i t y Grade 23 Maximum Favourable Grade 24 Minimum Grade 26 V e r t i c a l Curves 27 Cross Sections 29 Road Width 30 Ditches 31 Side Slopes 32 S o i l Properties as They Af f e c t Side Slopes 33 I I I . LOCATION METHODS 37 IV. EARTH ALLOCATION METHODS 39 MASS DIAGRAM 40 EARTH ALLOCATION BY LINEAR PROGRAMMING 42 Linear Programming 42 Assumptions of Linear Programming 43 Ch a r a c t e r i s t i c s of Linear Programming 44 Linear Model of Mass A l l o c a t i o n Problem 45 Constraints 46 Reason for Using Linear Programming 48 V. DESCRIPTION OF THE STUDY OBJECT 50 VI. COMPUTATION OF EARTH ALLOCATION 53 TRANSFORMATION PROGRAM 53 VOLUME CALCULATION AND ALLOCATION 56 Data f o r The Linear Programming Formulation 58 Computation of Excavation Cost 59 Production 61 Hourly Rate of The D9 Operation 62 Haul 64 VII. ANALYSIS OF EARTH ALLOCATION 68 ANALYSIS OF MASS DIAGRAM 68 ANALYSIS OF LINEAR PROGRAMMING SOLUTION 69 Ite r a t i o n s 69 Optimum Volume A l l o c a t i o n 70 Earth Moving S t a t i s t i c s Obtained by Linear Programming . 70 Minimum Earth Moving Cost 71 TOTAL COSTS: MASS DIAGRAM VERSUS LINEAR PROGRAMMING 71 VIII. SUMMARY AND CONCLUSION 74 IX. SUGGESTIONS FOR FURTHER RESEARCH 76 BIBLIOGRAPHY 77 APPENDICES 80 Figure page 1 Free-body Diagram of a Truck on a Superelevated Road 10 2 Curve Widening Due to Truck and T r a i l e r 17 3 Terminology on Cross Section 30 4 Typical Cross Section 35 5 Headings f or The Volume and Distance Calculations of The Stati o n - t o - s t a t i o n Method 39 6 Grade Breaks: V e r t i c a l Measurements 54 7 Grade Breaks: Horizontal Measurements 55 8 Summary of Total Earth A l l o c a t i o n Costs 71 Appendix page 1 Transformation Program 80 2 Volume C a l c u l a t i o n 98 3 Linear Programming A l l o c a t i o n 101 4 Mass Diagram 137 5 Location of Road C 138 The costs of road construction, road maintenance and hauling account f o r up to 7 5 % of the t o t a l costs of logging. The major cost of forest road construction i s associated with earthwork. However, minimizing volume of excavation does not imply automatically mini-mized earth moving cost. Two roads of any length with the same v o l -ume of earthwork w i l l have d i f f e r e n t cost depending on the sum of transportation distances. Earthwork i s composed of two optimization problems, which should be integrated. F i r s t l y , excavation must be minimized, which i s obtained by optimum road lay-out. Secondly, there i s the problem of optimum earth a l l o c a t i o n between st a t i o n s . F i l l , cut, waste or borrow must be optimized based on earth moving cost. Optimizing each problem separately often r e s u l t s i n a sub-optimization of the whole system. It i s d i f f i c u l t to look at e n t i r e systems without the aid of mathematical models. Based on t r a d i -t i o n a l methods, a new approach of volume a l l o c a t i o n i s presented according to the c r i t e r i a of minimizing earth a l l o c a t i o n cost using LP, and a comparison i s made with the most commonly used mass d i a -gram method. The introduction of the mass diagram by Goering was a great improvement i n t r a d i t i o n a l s t a t i o n - t o - s t a t i o n earth volume a l l o c a -t i o n . The mass diagram i s a semi-graphical method of earth a l -l o c a t i o n and determines d i r e c t i o n of haul and the amount of volume hauled. Inaccuracies may occur due to the natural lack of p r e c i s i o n of graphical s o l u t i o n s . Boughton (1966) proposed f i r s t to minimize the earth a l l o c a -t i o n volume using the LP technique. However, in h i s approach regions of excess cut or regions of extra f i l l were not subdivided, but were treated as contiguous units. - This approach r e s u l t s in neglecting the earth moving cost. T h i s t h e s i s t r i e s to improve on the accuracy of Boughton's so l u t i o n by considering the haul and the net volume at each s t a t i o n . The earth a l l o c a t i o n costs are ca l c u l a t e d using excavation cost plus the transportation cost between p a r t i c u l a r cut and f i l l s t a t i o n s . In t h i s way, the r e s u l t s of the LP method and the mass diagram could be compared. I I . GEOMETRIC ROAD DESIGN ELEMENTS Road design elements are the geometric f a c t o r s to be considered when designing a forest haul road. The design elements here con-sidered are: - h o r i z o n t a l alignment - v e r t i c a l alignment - cross s e c t i o n s . The determination of the optimal combination of values f o r these design elements, f o r any p a r t i c u l a r haul road, requires a thorough understanding of the purpose of the road, the physi c a l and mechanical c h a r a c t e r i s t i c s of the vehicles that w i l l use i t , and the properties of the s o i l through which the road w i l l be b u i l t . The remainder of t h i s chapter deals with the r e l a t i v e importance of the design elements l i s t e d above and t h e i r d e r i v a t i o n f o r a main road in the U n i v e r s i t y of B r i t i s h Columbia Research Forest. FOREST MAIN HAUL ROADS A forest main haul road often i s a permanent all-weather road f o r the execution of forest management. It must provide f o r a safe and economic t r a f f i c flow over i t s e n t i r e length. LAND SERVICE A f o r e s t main haul road, as a means of access to forest land, i s of main importance as i t i s the backbone to the network c o n s i s t i n g of lower standard forest roads. In i t s design prime consideration i s given to fa s t transportation by vehicles between points, such as landings, dumps, and m i l l s . The s i g n i f i c a n t service functions of a main haul road i s to provide easy access f o r equipment and personnel to perform functions r e l a t e d to management, s i l v i c u l t u r e , and protection of the forest t r a c t . ECONOMIC OBJECTIVE The economic objective i n haul road design implies a minimum t o t a l cost f o r road construction, f o r maintenance of the road and the vehicles using i t , and f o r the transportation of goods and serv-i c e s . The measure of economic transportation of logs i s based on speed and load (weight or volume). Hauling costs are expressed i n d o l l a r s per u n i t weight or volume. Finding the minimum t o t a l cost of road construction, maintenance for road and ve h i c l e s , and hauling cost i s not dealt with i n d e t a i l i n t h i s t h e s i s . This t h e s i s approaches the problem of minimizing earthwork cost only. ENGINEERING CHARACTERISTICS OF MAIN FOREST HAUL ROADS t r a f f i c Flow and Density T r a f f i c on main haul roads c o n s i s t s mainly of heavy duty equipment such as logging trucks, maintenance and service v e h i c l e s . The t r a f f i c flow, because of generally low volume, i s r a r e l y i n t e r -rupted. Company owned roads, operated on a pr i v a t e or semi-private b a s i s , are closed to public during working hours. In regard to the d i r e c t i o n of t r a f f i c flow on a forest road, there i s a one way flow f o r loaded trucks to the dumps and return t r i p s of empty trucks to the landings. The average d a i l y t r a f f i c depends on the s i z e of a p a r t i c u l a r logging enterprise and varies considerably. There i s much l e s s t r a f f i c on a forest road than on a pu b l i c road of comparable design. A t r a f f i c density on forest main haul roads of 100 to 1000 vehicles per day i s not uncommon. This corresponds to 25 to 250 loads leaving an operation per day. Speed Speed i s denoted for road design purposes as design speed. Design speed has been defined by the American Association of State Highway O f f i c i a l s as the maximum safe speed that can be maintained over a section of road when conditions are so favourable that the design features of the road govern. The U. S. Forest Service bases a l l economic c a l c u l a t i o n s on design speeds of 45 mph and 50 mph for loaded and empty trucks re-spe c t i v e l y (Logging Handbook, 1960). Speeds up to only 40 mph are considered i n the Forest Engineering Handbook (U. S. Department of the I n t e r i o r , 1964). Adamovich and Webster (1968) assumed a design speed of 35 mph f o r main haul roads i n the U n i v e r s i t y of B r i t i s h Columbia Research Forest. Weight of Vehicles The maximum gross v e h i c l e weight (GVW) of loaded logging trucks i s li m i t e d by the truck capacity and bearing capacity of the road. Maximum o f f highway GVW i s 250,000 pounds composed of a truck tare weight of 70,000 pounds and a load of 20,000 fbm or 180,000 pounds on a basis of 9 pounds per fbm. The advantage of high loading c a p a c i t i e s i s that more volume i s hauled per round t r i p and fewer trucks are required for trans-p o r t a t i o n of the same volume. However, increased GVW increases road construction and maintenance cost. Optimum vehic l e weight should be considered as the one r e s u l t i n g in minimum t o t a l cost of transport, road and v e h i c l e cost. Research would be required to investigate the interdependencies. OPTIMUM ROAD STANDARDS To select the optimum standard of a road, the minimum t o t a l y e arly cost i s considered which i s the sum of amortization cost and the i n t e r e s t on the investment, maintenance and hauling costs. Forest road h i s t o r y i n Europe, e s p e c i a l l y in Bavaria, Germany, shows that many p r i v a t e forest roads changed t h e i r status to p u b l i c f o r e s t roads. Some of them f i n a l l y were developed into p u b l i c high-ways. The same trend can be seen now i n B r i t i s h Columbia, were some p r i v a t e , company owned roads have changed to semi-private roads with l i m i t e d p u b l i c access. Thus, i f i n doubt about choosing between two standards f o r a future main haul road, which could develop into a p u b l i c road, the higher standard should be selected, i f the government would pay the increased cost. Selection of Design Elements The s e l e c t i o n of the design elements depends on the goal and c h a r a c t e r i s t i c s of a p a r t i c u l a r road. Those for forest main haul roads have been defined in the previous chapter. Based on these assumptions the required minimum physical standards can be defined f o r the h o r i z o n t a l and v e r t i c a l alignment o f the road and also f or i t s cross section. Horizontal Alignment Horizontal alignment i s the h o r i z o n t a l d e f l e c t i o n of the tangents between the s t a r t i n g point and the end point v i a intermediate co n t r o l points. Horizontal curves are smooth t r a n s i t i o n s from one tangent to the next one. The number of curves per unit length of the road, as well as the r a d i i of the curves s i g n i f i c a n t l y influence the t r a v e l speed, which in turn, influences the round t r i p time and operation cost (Logging Road Handbook, 1963). Horizontal alignment i s a function of topog-raphy, s o i l , v e h i c l e design and speed. The curves are u s u a l l y c i r -c u l a r curves and are s p e c i f i e d e i t h e r by t h e i r r a d i i or t h e i r degree of curvature. Superelevation i n Curves Superelevation i s defined i n two ways and used interchangeably i n t h i s text. Superelevation i s the r a t i o of the v e r t i c a l distance between the heights of inner and outer edges of road surfaces and the h o r i z o n t a l p r o j e c t i o n of the road width, or the angle between a h o r i z o n t a l plane and the road surface i n degrees. Superelevation i s generally j u s t i f i e d i n order to keep the design speed i n curves at the same l e v e l as on adjacent tangents. This r e s u l t s i n uniform speed, and therefore economic timber trans-po r t a t i o n . However, superelevation i s a d e f i n i t e hazard to slow moving v e h i c l e s , and, when i c y conditions p r e v a i l . According to the Manual of Geometric Design Standards f o r Canadian Roads and Streets (1967) and Edwards and Townsend (1961) a maximum superelevation of 0.08 may be applied. For design speeds below 35 mph in forest road design, superelevation can be neglected i f the road surface conditions permit. Side F r i c t i o n Factor The side f r i c t i o n f a c t o r i s a measure of the tendency of a vehicle not to move perpendicular to i t s d i r e c t i o n of t r a v e l when acted upon by c e n t r i f u g a l forces. The side f r i c t i o n f a c t o r i s governed by the speed of the ve h i c l e , i t s t i r e s , and the c h a r a c t e r i s t i c s of the road surface (Meyer, 1967). The higher the side f r i c t i o n f a c t o r , the greater the degree of curvature allowable without decreasing the design speed even without superelevation. This means, that the road c e n t e r l i n e may follow ridges, and g u l l i e s much c l o s e r . Minimum Radius Due to Design Speed - Background Theory The theory of superelevation must be defined i n order to determine the maximum allowable degree of curvature f o r a given design speed. Figure 1. Free-body diagram of a truck on a superelevated road Figure 1 shows a free-body diagram of a truck on a super-elevated section of road. The following i s a der i v a t i o n of the side f r i c t i o n f a c t o r as a function of superelevation and vehicle weight. The forces wx (weight component p a r a l l e l to road surface) and c x ( c e n t r i f u g a l force component p a r a l l e l to road surface) are c r i t i c a l f o r s l i p p i n g sideways. From a vector analysis of Figure 1, i t can be seen that: s i n cx =» — or wx «= s i n cx • w and w c x cos cx = — or c x •> cos cx • c c where w « GVW i n pounds wx « weight component p a r a l l e l to road surface i n pounds Wy = weight component perpendicular to road surface i n pounds CX = angle i n degrees between actual road surface and h o r i -zontal plane (superelevation) c x = c e n t r i f u g a l force p a r a l l e l to road surface i n pounds Cy •= c e n t r i f u g a l force perpendicular to road surface i n pounds wv2 c => c e n t r i f u g a l force; c <= — — GR where v =» speed in feet per second G = gr a v i t y , 32.23 feet :per second squared R = radius of curve in feet T r a v e l l i n g at equilibrium speed means equilibrium between the forces wx and c x and SP X = 32y = 0. Under these conditions no s l i p p i n g occurs even on surfaces without f r i c t i o n . The permissible superelevation as a function of design speed and curve radius can be derived as follows (Meyer, 1967): w x - c x 2 sine* • w = cos <x • c but c « 2Y_ so that GR 2 wv sincx • w = cos w * where cos W = 0.996 f o r GR maximum superelevation, and becomes cos cx = 1 v 2 s i n cx » (Meyer, 1967) GR where v = v e l o c i t y i n feet per second G = g r a v i t y , 32.23 feet per second squared R • radius of curve in feet ot = superelevation i n degrees Thi s i n d i c a t e s , that the amount of superelevation i s independent of vehicle weight i n the case of equilibrium of the forces wx and c x . When the forces p a r a l l e l to the road surface are not in equilibrium, then the vehic l e has a tendency to move l a t e r a l l y . T h i s tendency i s expressed as the r a t i o of the sum of the forces p a r a l l e l to the road surface and the forces perpendicular to i t . It i s measured by the side f r i c t i o n f a c t o r and i s defined as follows: (w • cos oc • f) + w s • s i n cx «• c • cos cx Solving the equation f o r f leads s to - . c x " w x - c • cos cx - w • s i n cx. s c„ + w„ - c • sinCX + w • costt Assume that 0< «• 0° then s i n 0° - 0 cos 0° =• 1 max O, =» 0.08 - 8% •» 4.6° Yield s the r e s u l t where f = side f r i c t i o n f a c t o r s a l l other symbols as above C a l c u l a t i o n of the Side F r i c t i o n Factor for Forest Roads Based on data and experience, the design manual (1967) gives a side f r i c t i o n f a c t o r of f g «• 0.165 f o r a design speed of 35 mph on blacktop. Based on forest road conditions and the formula developed above, the side f r i c t i o n f actor becomes: 2 9 WV O I f c• . GR] _ v . U.A67 » 35) s " w w G • R . 32.23 • R . nun mm f „ 81.796 s Rmin where R =» minimum radius of curve in feet which must be m i n determined . a l l other symbols as above The side f r i c t i o n f a c t o r on forest roads can be assumed to be 60% of the c o e f f i c i e n t of f r i c t i o n i n l i n e of t r a v e l . On dry firm gravel, u s u a l l y on main haul roads, the c o e f f i c i e n t of f r i c t i o n equals f = 0.8 (Adamovich, 1970). Thus, the side f r i c t i o n f a c t o r i s f - 0.6 • f s f 0.6 • 0.8 s f 0.48 s Maximum Degree of Curvature Knowing the values of design speed, superelevation and side f r i c t i o n f a c t o r , the degree of maximum curvature can be ca l c u l a t e d according to the following formula, based on previous equilibrium equations: D » maximum degree of curvature = 5730 j R e • superelevation i n tangent value f = side f r i c t i o n f a c t o r s v •» design speed i n mph » speed i n f t / s e c j 1.467 Using the maximum values f o r the formula provides the maximum degree of curvature. D = 85,944 (e + f g ) - (Design Manual, 1967) where D max 85,944 (0.48) 35 • 35 41,253.12 1225 D 33.7° - 34° max The maximum degree of curvature corresponds to a minimum radius of 5730 5730 R •= D 33.7 R - 170 feet The maximum allowable degree of curvature on forest roads i s more than twice the one allowed f o r highways of the same design speed. T h i s i s due to the d i f f e r e n c e s of the f r i c t i o n f a c t o r s as a function of road surfaces. Curve Widening Curve widening i s an important f a c t o r , because i t influences the volume of earthwork to a great extent. When a vehicle negotiates a curve, the rear axles t r a v e l on a curve of a smaller radius than the front axles. The d i f f e r e n c e of the r a d i i depends on the degree of curvature and vehi c l e design. Diagrammatically t h i s may be rep-resented as shown i n Figure 2. R, wi = widening due to truck W2 0 widening due to t r a i l e r w = w1 + w2 = t o t a l widening Figure 2. Curve widening due to t r a c t o r and t r a i l e r Considering the t r a c t o r only, one obtains the following r e s u l t s : sin CX w, S3 A LI T w l M. m^in 2 L l w i ^ ^ i n L i and s i n (X - ^ y i e l d Kmin T . L l or -y- w l * ^min 8 1 1 1 1 s < > l v e c l f o r w i (due to t r a c t o r only) Considering the t r a i l e r only, the curve widening i s derived as follows: sin (3 = — and s i n (J =» ^2 y i e l d h i R l w 2 L 2 I", -— = _± and w, • Ri = Lo * —L r e s u l t i n a widening L_2 Ri 1 1 * 2 2 L 2 w 2 = 3 (due to t r a i l e r only) 2 R 1 Combining these two r e s u l t s we obtain the following t o t a l widening due to t r a c t o r and t r a i l e r : W •» Wj + W2 L i 2 L 2 2 w = + (due to t r a c t o r and t r a i l e r ) 2Rmin 2Ri but Rj •= / R j j j j ^ - L ] ^ and w becomes L ! 2 L 2 2 w = + , 8 t li 2Rmin 2 / R ^ n ^ L ? where w «• curve widening i n feet = wheel base of t r a c t o r i n feet L2 = wheel base of t r a i l e r only i n feet ^min ™ m i n i m u m radius of curve i n feet = radius of curve followed by the rear truck axles The wheel bases of coastal logging trucks with extended reach are = 17.5 feet and Lj " 47.0 feet f o r t r a c t o r and t r a i l e r respec-t i v e l y . (17.5)2 . (47.0)2  w a + — and 2Rmin 2R! 306.25 2209  wmax " 2(170) + 2^(170)* - (17.5)z 30^25 + |g?^0 m 0 > 9 + ^ 340.00 338.2 wmax - 7 ' 4 f e e t The widening remains a function of the curve radius. Several empirical formulae heve been developed f o r easy c a l c u l a t i o n of curve widenings. w m (Adamovich, 1970) w « S^P_ (u. S. Forest Service, Oregon) w - R - nVR - h + The f i r s t two formulae are v a l i d f o r fo r e s t roads, the t h i r d i s used i n highway design, taking the numbers of lanes (n) and the design speed (v) into account. V e r t i c a l Alignment A forest road u s u a l l y connects points that d i f f e r i n eleva-t i o n . Also, i n connecting these points i t must pass through areas of broken topography and i s often constrained to pass through cer-t a i n s p e c i f i c points such as v a l l e y s and saddles known as cont r o l p oints. The r e s u l t i n g f l u c t u a t i o n i n grades thus required, and the v e r t i c a l curves f o r smooth t r a n s i t i o n between d i f f e r e n t grades, are known as the v e r t i c a l alignment of the road. Proper v e r t i c a l a l i g n -ment takes i n consideration problems of sight distance, stopping distance, ve h i c l e capacity and surface erosion. Grades The proper choice of maximum grades i s very important as they a f f e c t s i g n i f i c a n t l y costs of earthwork, road maintenance and hauling. Steep maximum grades decrease earthwork as the road c e n t e r l i n e f o l -lows the topography very clos e but increases road maintenance and operation costs. Grades are expressed i n per cent and are the r a t i o (tangent) of the v e r t i c a l distance and hori z o n t a l p r o j e c t i o n of the actual road length m u l t i p l i e d by 100. Increased grades permit attainment of points at d i f f e r e n t elevations i n a shorter distance, which i n some cases avoids switchbacks. However, truck speeds w i l l be reduced and maintenance cost of road and veh i c l e s w i l l be i n -creased. Due to the c h a r a c t e r i s t i c s of the one way t r a f f i c flow of loaded and empty trucks on forest roads, a d i s t i n c t i o n i s made be-tween a favourable and an adverse grade. A favourable grade denotes a grade downhill, and an adverse grade a grade u p h i l l , f o r a loaded truck. Maximum Adverse Grade Maximum adverse grade i s reached, when the t r a c t i v e e f f o r t i s equal to the sum of road resistances without acceleration or decceleration and i s l i m i t e d by the f r i c t i o n f a c t o r f o r t r a c t i o n , that i s when the wheels would s l i p . Fast transportation i s possible at grades, which allow the engine to turn at f u l l horsepower r a t i n g . Waelti (1960) suggested a maximum adverse grade of 6% under general coastal conditions and a design speed of 35 mph f o r coastal logging trucks. Adamovich (1968) proposed the same value f o r the s p e c i f i c conditions of the U n i v e r s i t y of B r i t i s h Columbia Research Forest. Maximum grades are calculated with the formula •max TE - w t% -. R c - RA 20wt where Pmax0 m aximum adverse grade i n per cent TE - t r a c t i v e e f f o r t i n pounds wt = GVW i n tons R^ =• r o l l i n g resistance i n pounds per ton R c « curve resistance i n pounds R. = a i r resistance i n pounds The t r a c t i v e e f f o r t i s a function of the torque, the transmis-sion and d i f f e r e n t i a l gear r a t i o and the e f f i c i e n c y of the engine. Thus, the t r a c t i v e e f f o r t w i l l be d i f f e r e n t f o r each gear. The t r a c -t i v e e f f o r t i s cal c u l a t e d as follows f o r d i r e c t speed: 375 • BHP « n TE - *- and TE - w^Rp + 20pw,- (Adamovich, t R t 1970) where TE «• t r a c t i v e e f f o r t i n pounds BHP = break horse power n •» e f f i c i e n c y of truck engine wfc « GVW i n tons R^ = r o l l i n g resistance i n pounds per ton p «• adverse grade i n per cent The speed i n the formula above i s based on the rimpull of the engine, which i s assumed to be 10,000 pounds f o r a standard logging truck used i n the U n i v e r s i t y of B r i t i s h Columbia Research Forest on an adverse grade. 10,000 pounds rimpull correspond to the second gear and a speed of 12 mph. Thus, the maximum adverse grade f o r a logging truck i s cal c u l a t e d f or the conditions men-tioned as follows: 3 7 5 • 325 - 0.8 = 4 5 t o n s . 6 Q £Oun|s + 4 5 t o n s . 2 Q p and solved f o r p y i e l d s ,175 • 325 • 0.8 45 » 60 O a s • - — — — — — a : 9-3 V 12 • 20 • 45 20 • 45 Pmax " 6 % V e l o c i t y Grade A v e l o c i t y grade i s a steeper than the maximum adverse grade f o r which the i n i t i a l momentum of the vehic l e at the beginning of the v e l o c i t y grade i s used to overcome the extra grade resistance. The i n i t i a l momentum on a true v e l o c i t y grade i s s u f f i c i e n t to over-come i t without s h i f t i n g gears. The maximum allowable v e l o c i t y grade i s calculated according to the following formula: n . n . s i 2 - s 2 2 where p Q »= v e l o c i t y grade i n per cent p r « maximum adverse grade i n per cent s^ «• speed at beginning of the v e l o c i t y grade i n mph s^ • speed at the end of the v e l o c i t y grade i n mph d v » ho r i z o n t a l distance of v e l o c i t y grade i n feet Use of v e l o c i t y grades makes i t po s s i b l e to overcome rapid change i n elevation over a short distance while s t i l l holding good alignment. T h i s r e s u l t s i n savings on construction cost and t r a v e l time, although increases maintenance costs. Maximum Favourable Grade Any favourable grade i s governed by the safe stopping distance. The stopping distance i s the shortest distance i n which a ve h i c l e can come from i t s t r a v e l speed to a complete stop. Stopping distance i s a function of re a c t i o n time of the d r i v e r , v e h i c l e speed and c o e f f i c i e n t o f f r i c t i o n of the road surface. The stopping distance i s calculated from the following formulae: D = T>i + D 2 where t • s • 1.467 s 2 D 9 = — 3 0 « - t5o> D = stopping distance i n feet » r e a c t i o n distance i n feet I>2 m breaking distance i n feet t = rea c t i o n time i n seconds s «• speed i n mph f = c o e f f i c i e n t of f r i c t i o n p <= maximum favourable grade 2 s D " t * s • 1.467 + p — 30(f - TO) 30<D - <t . s . 1.467)) „ 1 ^ s o l v e d f Q r s 2 f - O.Olp s 2  P - ( f - 30<D - ( t . s • 1.467)) ) ' 1 0 0 s 2 P " l 0 0 < f ' TRJ'D - 44.0 • t • s } where f =0.35 f o r wet gravel s = 35 mph design speed D 250 feet t = 1.5 seconds 1225 P 100(0.35 - 7500 - 2310 P 11% Waelti (1960) proposed 8% maximum favourable grade f o r coa s t a l conditions. For the conditions i n the U n i v e r s i t y of B r i t i s h Columbia Research Forest Adamovich and Webster (1968) u t i l i z e d 10% as a maxi-mum favourable grade. Minimum Grade A road i s as good as i t s drainage, because water reduces the bearing capacity of the subgrade. Thus, poorly drained roads are expensive i n maintenance and have a short l i f e s p a n . No road should . be designed with zero per cent grade. In terms of hauling cost, the U. S. Forest Service found a maximum t r a v e l speed at 1.5% favourable grade. In terms of road maintenance the maximum grade occurs when s i l t i s j u s t eroded. S i l t i s a very f i n e and important binding material and i s eroded at grades greater than 1% i f not i n mixture with other p a r t i c l e s i z e s . ( V e r t i c a l Curves When the algebraic d i f f e r e n c e of the following grade and the approaching grade i s p o s i t i v e , then the v e r t i c a l curve i s denoted as a sag curve; i f the d i f f e r e n c e i s negative, i t i s denoted as a crest curve. The length of crest curves i s a function of the adjacent grades and the sight distance f o r safe stopping. L - n - 2 o o «r*l (Meyer> 1 9 6 7 ) where L . =» minimum length of v e r t i c a l curve in feet min A = algebraic d i f f e r e n c e of adjacent grades, following grade minus approaching grade S =• sight distance in feet h^ = height of truck d r i v e r ' s eye; hj^ « 7 feet • height of obstruction on the road; h'2 " 0,3 feet The formula f o r the length of crest curves i s : A • S 2  Lmin " 200 (2.65 -f 0.17) 2 The formula might be s i m p l i f i e d more by assuming that the sight distance equals the stopping distance. where xs: B " -^j^ (Manual of Geometric Design Standards, 1967) R o s • t • 1.467 B + R B = braking distance i n feet R = reaction distance i n feet s = speed i n mph; design speed = 35 mph f «= c o e f f i c i e n t of f r i c t i o n ; f = 0.35 t » reaction time in seconds; t = 1.5 seconds S = stopping distance i n feet The stopping distance f o r f i r s t c l a s s forest road conditions S - § T - 0 T 3 i + 35 ' 1.5 • 1.467 193 feet Su b s t i t u t i o n i n the foregoing formula leads to: A(193) 2 A * 37,249 m i n 1590 m i n 1,590 L - 23.4 A min T h i s r e s u l t implies that the length of a crest curve f o r coastal conditions i s 23.4 feet per 1% d i f f e r e n c e of adjacent grades. T h i s f i n d i n g agrees with the most commonly used p r a c t i c e that the grade change per 100 feet should not be more than 6%. The above formula i s applied only as a guideline; the engineer may decide to deviate from i t due to the t e r r a i n but never at the expense of safety. Cross Sections The shape of the cross section determines to a great extent the earthwork required. The road width and the side slope r a t i o s are of main importance. The road width i s the width of the running surface, the shoulders and the d i t c h . Figure 2 i l l u s t r a t e s the terminology of cross sections. l : f — — 71 r i g h t of way Figure 3;. Terminology on Cross Section Road Width The road width i s a function of safety, drainage, speed, and type and number of vehicles t r a v e l l i n g on a f o r e s t road. The road width must be at l e a s t equal to the veh i c l e width. A l a t e r a l band at e i t h e r side of the running surface f o r l a t e r a l support of the ve h i c l e s reduces maintenance cost f o r both road and v e h i c l e s , and increases t r a f f i c safety. Dense t r a f f i c may necessitate a multiiane road. In f o r e s t r y the d e c i s i o n on the number of lanes i s based on the volume hauled. Unfortunately, no accurate c r i t e r i a has been developed todate. The B r i t i s h Columbia Forest Service (Waelti, personal communication) i s studying the spacing of turnouts f o r a given speed and given number of vehicles to f i n d an answer which would optimize earth-work and truck speed. T e r r a i n and s o i l must also be considered f o r choosing a p a r t i c u l a r road width, since these two f a c t o r s a f f e c t earthwork to a large extent. Ditches The d i t c h accumulates the water flowing from the side slopes towards the road and the water from the road surface. A d i t c h must be on any cut along a main haul road to ensure adequate water run o f f to avoid decreased bearing capacity of the subgrade and reduce f r o s t heaves. C a l c u l a t i n g the d i t c h width involves many uncertain variables such as area of watershed, grade changes, c u l v e r t spacing, r a i n f a l l , and roughness c o e f f i c i e n t s of the d i t c h . Due to the number and uncertainty of these v a r i a b l e s , an empirical so l u t i o n of the d i t c h dimensions i s j u s t i f i e d . There are two types of d i t c h dimensions proven adequate f o r the research f o r e s t according to the s o i l c h a r a c t e r i s t i c s . In rook, the di t c h width i s 2 f e e t , i n common material 3 f e e t . The d i t c h depth i n both materials i s 1 foot. A wide d i t c h r e s u l t s i n a greater road width and increased excavation and consequently increased earth moving. The d i t c h depth i s not rela t e d to volume c a l c u l a t i o n s , because i t i s excavated by a grader or blasted and a f f e c t s the road construction cost only to a minor extent. Deep ditches would be expensive to construct and maintain. Side Slopes The side slopes are the slopes of the cuts and / or f i l l s j o i n i n g the road surface. Side slopes are denoted as the r a t i o of the h o r i z o n t a l distance to one un i t of v e r t i c a l distance or the cotangent of the slope angle. The o b j e c t i v e i s to construct side slopes as steep as possible without inducing the danger of s l i d e s and without impairing the sight distance i n order to reduce earthwork. The maximum allowable side slope i s a function of s o i l composition and density. F i l l and cut have d i f f e r e n t side slope r a t i o s due to d i f f e r e n t compaction. Modern equipment working on new f i l l s compacts common material to a higher density than ^n s i t u . S o i l Properties as They Af f e c t Side Slopes The best angle of a side slope for a given l o c a t i o n can only be determined through a d e t a i l e d analysis of the s o i l . The following considerations are based on undisturbed and untreated s o i l . Side slopes depend on the shear strength that the s o i l can withstand. Shear strength i s composed of f r i c t i o n , which i s the resistance due to i n t e r l o c k i n g of p a r t i c l e s , and cohesion, which rep-resents the forces which hold the p a r t i c l e s together. Cohesive forces are of chemical and e l e c t r i c a l nature. The resultant of these forces i s the angle of the slopes as established n a t u r a l l y . This angle i s c a l l e d the angle of repose. The shear strength i s expressed by Coulomb's Law (Capper and Cassie, 1963). s = c + t • tan C X where C X = angle of i n t e r n a l f r i c t i o n , in degrees, approximately equal to the angle of repose c •» cohesion i n pounds per square inch t = normal stress in pound per square inch s «• s o i l shear strength in pound per square inch Solving the equation for the angle of repose: tan (X » s ~ 0 t Angles of repose f o r rock and loess are close to 90 due to very high cohesion. Weathering reduces cohesion to such an extent, that a side slope must be applied for safety of the t r a f f i c . For f i n e material with low cohesion and almost no f r i c t i o n , such as wet c l a y , o angles of repose are as low as 10 , which corresponds to a side slope r a t i o of 5 : 1. Cut and f i l l slopes in average common material and rock are u s u a l l y based on past experience. t This i s the approach used by Adamovich and Webster (1968) in the proposal f o r slope r a t i o s in the U n i v e r s i t y of B r i t i s h Columbia Research Forest (Figure 4). The shape of natural slopes i s always s l i g h t l y concave. The engineer at the actual construction s i t e must take advantage of t h i s fact by excavating more material than required close to the road and l e s s at the f a r end of the side slopes. T h i s strategy has a cost reducing e f f e c t due to a reduction in earth moving without impairing safety. However, t h i s strategy does not hold for a l l s o i l s and must be tested under each new set of conditions. 1 1 I i j i 1 1 1 1 i 1 ~ ~ r " 1 | i I i I 1 i | 1 is l ! 1 I 1 j ! 1 1 1 t i i i 1 ; 1 ! i j 1 ! i i ! vl -it-. :p i I L L L I XCL i u K ll -LU.l - 1 1 i i ! i — i } j . 1 1 i i | _ i _ . " 1 j . L. 1 !CZ ? " J , i 1 I *S oc X tlOf ur.i. L LfJ irr C M- JILL it • 1 1 1 1 1 ! I i 1 ] 1 • I 1 1 1 1 11 1 1 1 1 I I i ,( 1 1 1 c ll t 'ill 1 1 (•! 1 i •r-1 rH T l I J i i ) V A- Jfir >c I \\ V | | | I i \ . 1 i r ..1 . L i I ' r i | r z eJtu .» s 1 1 1 i ! i i . • i i ! i i <* j | r T X f 1 i I I H £> 1 \ V T I 1 i j i i I T ; gun »_ -5 t-T-yp-i C a t s. t*1-A r n 1 " 1" t 1 | I 1 — 1 —+— 1 1 1 1 i 1 1 i 1 1 1 1 11 i i i < I 1 1 1 •! I_I_T_J_ _L. i • I I I . LOCATION METHODS Location methods are techniques by which the forest engineer determines the l i n e of a future road. The most common location methods in f o r e s t r y are the highway engineer's method, and i t s modification fo r logging engineers, the contour o f f s e t method and the d i r e c t loca-t i o n method (Pearce, 1964). The se l e c t i o n of one of these methods depends on the proposed standard of the road, the topography, the supervision during construction and experience of the loc a t i o n engineer. i The f i r s t step of every location method i s the reconnaissance of the area. Then, the decision i s made as to the c l a s s of the survey to be conducted. A higher c l a s s w i l l be chosen in cases of high standard roads, d i f f i c u l t t e r r a i n , good engineering supervision during construction and with le s s experienced personnel. Except f o r the d i r e c t l o c a t i o n method, a preliminary l i n e (P-line) i s run and staked, a f t e r which the elevation of the stakes i s measured. The topography i s taken at a l l stations on d i f f i c u l t t e r r a i n or at every s t a t i o n in the case of high c l a s s surveys. The P - l i n e , the elevation of stations and the topography provide the necessary information f o r e s t a b l i s h i n g a contour s t r i p map f o r the lo c a t i o n survey l i n e . Based on the c r i t e r i a of minimizing earthwork, t r i a l p r o f i l e s are proposed. Areas are calculated and volumes based on the end area formula. Using a tabulated form for volume d i s t r i b u -t i o n , the s t a t i o n - t o - s t a t i o n values of excavated material to be used on the s i t e , excess cut, need in f i l l s , waste and borrow are decided on. Once the volume d i s t r i b u t i o n s a t i s f i e s the required standards, the l o c a t i o n survey l i n e i s f i x e d and i s ready f or l a y i n g out in the f i e l d . Staking of the lo c a t i o n survey l i n e , the side slopes, and sometimes the r i g h t of way, terminates the planning stage of the road. IV. EARTH ALLOCATION METHODS For comparing alternate route p o s s i b i l i t i e s , the so c a l l e d "design mass graph" can be used, which has been developed by the B r i t i s h Columbia Forest Service. The volume estimate i s based on previous construction and experience. The most p r i m i t i v e method of earth a l l o c a t i o n i s done by determining volumes and balance points based on the p r o f i l e only. However, t h i s method i s inaccurate and used only for preliminary cost estimates. The s t a t i o n - t o - s t a t i o n method i s a numerical method which allows a quick volume and cost analysis using desk c a l c u l a t o r s . The balance points between cuts and f i l l s are determined, and the haul distances checked. C a l c u l a t i o n of the freehaul and overhaul allows compilation of distances f o r the construction equipment to be used, and therefore the costs. In the table below the headings for volume and distance c a l c u l a t i o n s are shown (Figure 5) Sta Area Al+Ao Dist y d i i II 3—, Volume yd Tota l volume used on s i t e ex-cess cut need in f i l l overhaul l'haul rock common rock common waste bos-row d i s t qu-ant e | f c j f c f c|f c|f c | f Figure 5. Headings f o r the volume and distance c a l c u l a t i o n s of the s t a t i o n - t o - s t a t i o n method This method has the great advantage of giving quickly the s i z e of the earthwork, but i s inaccurate and ari t h m e t i c a l errors can e a s i l y occur: checking i s necessary. The s t a t i o n - t o - s t a t i o n method can e a s i l y be computerized which eliminates the ari t h m e t i c a l e r r o r s . Part of the B r i t i s h Columbia Forest Service program, based on t h i s theory, c a l c u l a t e s volumes (Appendix 2 ) . These volumes were l a t e r used as an input f o r the LP program (Appendix 3 ) . MASS DIAGRAM The mass diagram i s a continuous graphical representation of net cumulative volumes of cuts and f i l l s on a road construction. It shows the volume balance points, the amount of haul and i t s d i r e c t i o n . This permits the e f f e c t s of changing volume a l l o c a t i o n i n terms of volumes and cost to be studied. A ho r i z o n t a l l i n e i n t e r s e c t i n g the mass diagram i s a balance l i n e , where the sum of cuts and f i l l s are equal. The length of the balance l i n e shows the haul distance, which i s u s u a l l y delimited by freehaul and maximum economic overhaul distance. The haul i s determined g r a p h i c a l l y and i s the area between the mass diagram and any balance l i n e . C a l c u l a t i o n of the average haul and the cost of earth moving in s t a t i o n yards,allows computation of the earth moving cost. F i n a l l y , the d i r e c t i o n of haul i s determined on the mass diagram (see Appendix 4 ) , based on the e f f i c i e n c y of the equipment used for construction. EARTH, .ALLOCATION BY LINEAR PROGRAMMING Construction of a road involves r e l o c a t i o n of earth due to the di f f e r e n c e of the shape of the te r r a i n , and the road cross sections, and l o c a t i o n of the road, which i s constrained by the alignment. Earth w i l l e i t h e r be removed from high sections (cuts) and deposited in low sections ( f i l l s ) or wasted. This process can be formulated ; as an a l l o c a t i o n problem of a l l o c a t i n g excess material to f i l l s . The optimization technique most commonly used for solving a l l o c a t i o n problems i s LP. Linear Programming LP f i n d s the optimum of a decision problem, which i s described by l i n e a r functions of variables (Dantzig, 1963; Simonnard, 1966). In mathematical notation, the d e f i n i t i o n of a l i n e a r program i s written as follows (Smythe, 1966; Hi11ier-Lieberman, 1968): max z = c x + c x +....+ c x 1 1 2 2 n n subject to a x + a. x +....+ a x r v b 11 1 12 2 In n 1 a 2 1 X l + a 2 2 * 2 + + V n W b 2 a x + a x +....+ a x A / b ml 1 m2 2 mn n m where z = objective function; i t i s the o v e r a l l measure of effectiveness x " d e c i s i o n variable or l e v e l of a c t i v i t y n = number of competing a c t i v i t i e s C j =• cost of one unit of a c t i v i t y j a^j= amount of resource i consumed per u n i t a c t i v i t y j b^ = amount of resource i a v a i l a b l e m = number of constraints of the system; t h i s number w i l l w i l l be at l e a s t equal to the number of scarce re-sources Assumptions of Linear Programming Five basic assumptions must be s a t i s f i e d i n order to use LP su c c e s s f u l l y as a v a l i d optimization technique (Dantzig,1963). - non n e g a t i v i t y : a p a r t i c u l a r a c t i v i t y cannot be negative, i t must be at least zero - a d d i t i v i t y : i n order to exclude in t e r a c t i o n s between a c t i v -i t i e s , which are e x p l i c i t e l y not permitted i n LP, the a c t i v -i t i e s must be additive with respect to the objective function and resource use - d i v i s i b i l i t y : f r a c t i o n s of the decision variables must be permissible; i f not, there exist d i f f e r e n t optimization a l -gorithms f o r integer and mixed LP - d e t e r m i n i s t i c : the cost c o e f f i c i e n t s ( c ^ ) , the amount of resource consumed ( a ^ ) , and a v a i l a b l e resource Cb^) for a c t i v i t i e s must be known constants - p r o p o r t i o n a l i t y : the input and the-output of an a c t i v i t y are proportional to the l e v e l of that p a r t i c u l a r a c t i v i t y . More e x p l i c i t e l y , the output of a system i s l i n e a r l y and d i r e c t l y proportional to the input. This assumption requires that the objective function and every constraint must be l i n e a r . C h a r a c t e r i s t i c s of Linear Programming The assumptions l i s t e d above put heavy r e s t r i c t i o n s on the use of LP. However, a l t e r e d LP techniques, and d i f f e r e n t optimization techniques permit the dele t i o n of some of these r e s t r i c t i v e assumptions. Despite these l i m i t a t i o n s , LP features, as an optimization technique, a number of unique advantages. The power of LP r e s u l t s from i t s a b i l i t y to solve large problems. Computer programs have been developed that can solve LP problems with up to 4095 constraints and the number of variables are only l i m i t e d by the t o t a l memory space of the computer system. The LP model i s in the form of simultaneous equations, which, a f t e r some modifications, are solved by simple techniques. Li n e a r Model of Mass A l l o c a t i o n Problem L e t t i n g x ^ denote the volume al l o c a t e d from cut s t a t i o n i to d f i l l s t a t i o n j , Cy the cost of moving one cu yd from cut s t a t i o n i to f i l l s t a t i o n j considering the haul distance, c^ the cost of bor-rowing one cu yd at a borrow p i t , b. the volume borrowed in cu yds, c w the cost of wasting one cu yd, w^  the volume wasted, then the l i n e a r function becomes: min ^ ^ c ^ x + ^ jc.b. + ^ c w j i i j i j J j 1 w i cut s t a t i o n , excess material f i l l s t a t i o n , material required cost of earth moving per cu yd over the distance d from cut s t a t i o n i to f i l l s t a t i o n j volume of material transported from cut i to f i l l j cost of borrow per cu yd where i = j = c b " bj => volume borrowed f o r f i l l j c„ = cost of wasting one cu yd at cut i Wj «s volume wasted at cut i Note that the second and the t h i r d terms of the objective function do not include distance, because the borrow p i t i s assumed to l i e within freehaul distance. The material wasted w i l l be at the place where i t occurs. Thus, there i s no transportation of material i n -volved. Constraints The sum of the material a v a i l a b l e from cuts and borrows equals the sum of material required in f i l l s and wasted. These equations are denoted as the material balance equations. Scuts + ^borrows = < f i l l s + ^waste These material balance equations are the c o n s t r a i n t s . There are two d i f f e r e n t cases with regards to volume d i s t r i b u t i o n at a s t a t i o n : f i l l or cut. The following f i g u r e s show a graphical rep-resentation of these two cases: cut: cut a v a i l a b l e at s t a t i o n i = X waste at s t a t i o n i = w f i l l required at stations j « J i j f i l l : ^ c u t s a l l o c a t e d to j 1*1J ^borrows allocated to j = Sb. f i l l i n g j f i l l required at s t a t i o n j » Xj Obviously, there i s no borrow at any cut s t a t i o n . Thus, the general material balance equation becomes: Ccuts - 0 = ^ f i l l s + Cwaste ^ c u t s - ^ f i l l s - iwaste » 0 This constraint i n mathematical notation i s : x i - 5 R X U ' W I ' ° where Xi = volume of cut a v a i l a b l e at s t a t i o n i r.j m cut volume from s t a t i o n i transported to f i l l s t a t i o n j j€R •= denotes those f i l l s t a t i o n s , j , that are within maximum economic overhaul distance of s t a t i o n i w. « volume wasted at s t a t i o n i 1 In the case, where f i l l i s required, there w i l l be no waste. This f a c t o r i s set to zero i n the general material balance equation: S c u t s + ^ borrows = ^ f i l l s + 0 ^ . f i l l s - 2cuts - ^borrows •» 0 This equation in mathematical notation as a constraint f o r LP becomes X - £. x - £ b - 0 j i€R i j 1 i where b. «= volume borrowed at s t a t i o n i within freehaul distance x.. = cut volume transported from s t a t i o n i to s t a t i o n j iOR ° denotes those cut s t a t i o n s , i , that are within maximum economic overhaul distance of s t a t i o n j X.. « volume of f i l l required at s t a t i o n j Reason f o r Using Linear Programming The formulation of the objec t i v e function and the constra i n t s demonstrated a l i n e a r r e l a t i o n s h i p . A l l d e c i s i o n variables were of a deterministic and fractional nature, which allows the use of a straight forward optimization technique looking for the optimum. At this stage, i t was decided to check the f e a s i b i l i t y of u t i l i z i n g LP. Investigation showed, that a l l the five basic assumptions of LP were satisfied. Furthermore, the problem could be run on the University of British Columbia computer f a c i l i t i e s under the MPS system. This ensured a fast and accurate solution. Based on these considerations, LP was used as the optimization technique for finding the optimal solution. V. DESCRIPTION OF THE STUDY OBJECT The road project used f o r i l l u s t r a t i o n purposes of the theory developed i n t h i s t h e s i s , i s road C i n the U n i v e r s i t y of B r i t i s h Columbia Research Forest. The proposed road C i s a forest main haul road and w i l l connect the main gates of the U n i v e r i s t y of B r i t i s h Columbia Research Forest with the camp at Loon Lake. The road l o c a t i o n i s shown in Ap-pendix 5. The road l o c a t i o n follows the propositions of the master-plan. Road C w i l l be one of the three main roads f o r fast access to the centers of the forest and to the two main camps. The material through which the road passes, i s b a s i c a l l y hornblende granite d i o r i t e rock. A l l t h i s rock must be blasted. T h i s layer i s covered by dense poorly weathered t i l l . The t i l l i s unsorted with a s i l t y - s a n d matrix, containing gravel and boulders up to two feet i n diameter. The t i l l i s generally impermeable. This layer may be removed with a bulldozer without a d d i t i o n a l equipment. The general aspect of the country i s moderately r o l l i n g with moun-tainous areas i n the north. The cross sections are eit h e r f u l l cuts or f u l l f i l l s , or sidewise cross sectioning both i n common material and rock. T h e t o t a l l e n g t h o f t h e p r o p o s e d r o a d w i l l b e 10,250 f e e t o r 1.94 m i l e s . T h e m a s s d i a g r a m i s c a l c u l a t e d u p , t o a n d i n c l u d i n g s t a -t i o n 50+70. T h e max imum g r a d e i s 10% a n d b e t w e e n t h e v e r t i c a l p o i n t s o f i n t e r s e c t i o n 32+80 a n d 46+75. T h e m i n i m u m g r a d e i s -1.6% a n d b e t w e e n t h e v e r t i c a l p o i n t s o f i n t e r s e c t i o n 8+50 a n d 17+80. T h e r e a r e t e n o o c u r v e s w i t h d e g r e e s o f c u r v a t u r e b e t w e e n 8 a n d 36 . A s h r i n k a g e o f 33 p e r c e n t o f t h e u n d i s t u r b e d common m a t e r i a l i s i n c l u d e d f o r t h e m a s s c a l c u l a t i o n s . S w e l l o f r o c k y m a t e r i a l f o r f i l l i s n o t c o n -s i d e r e d . I t w a s f e l t , t h a t l o s s o f m a t e r i a l a t t h e s t e e p s l o p e s w i l l c o m p e n s a t e s w e l l . R o a d C h a s b e e n p r o p o s e d t o d e v e l o p t h e s e c o n d g r o w t h s t a n d b e t w e e n B l a n e y C r e e k a n d r o a d F . T h e s t a n d s t o b e d e v e l o p e d a r e c o m -p o s e d o f D o u g l a s - F i r , ( W e s t e r n H e m l o c k a n d W e s t e r n ( R e d c e d a r . T h e r o a d w a s l o c a t e d b y P r o f e s s o r A d a m o v i c h . A l l c a l c u l a t i o n s a r e b a s e d o n h i s f i e l d d a t a . A d a m o v i c h a n d W e b s t e r (1968) s u g g e s t e d r o a d d e s i g n s t a n d a r d s i n t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a R e s e a r c h F o r e s t . T h e s e s t a n d -a r d s h a v e b e e n c h o s e n a c c o r d i n g t o t h e p r i n c i p l e s d i s c u s s e d i n t h e c h a p t e r o n d e s i g n e l e m e n t s . The road design standards f o r the main haul road C in the U n i v e r s i t y Research Forest are: design speed 35 mph hori z o n t a l sight distance 250 feet sight distance f o r v e r t i c a l curves 300 feet absolute minimum radius 150 feet minimum radius due to design speed 250 feet surface width 20 feet d i t c h width i n s o i l 3 feet The following road design standards were used d i r e c t l y as computer inputs: o widening i n curves 1 foot per 10 curvature maximum favourable grade 10% maximum adverse grade 6% subgrade width 26 feet d i t c h width i n rock 2 feet d i t c h depth 1 foot d i t c h slope 5 : 1 side slopes as shown in Figure 4 VI. COMPUTATION OF EARTH ALLOCATION A computer i s very s u i t a b l e f o r reducing a great amount of tedious computations. A large number of computations due to changes of the center l i n e i s involved i n volume c a l c u l a t i o n s thus making the computer an excellent t o o l f o r forest road planning. There are three consecutive computer programs involved f o r optimization of earth a l l o c a t i o n by LP. Each program produces input f o r the following one. The f i r s t program reads the raw f i e l d data and allows entrance of data in a few d i f f e r e n t formats. Then i t transforms the data into a standard form which w i l l be the standardized input f o r the second program. This program c a l c u l a t e s the volumes which are the basis f o r the mass diagram and input f o r the LP program. TRANSFORMATION PROGRAM The f i r s t program reads the f i e l d data. I t reads the accumulated chainage to the nearest foot, the elevation of the center l i n e to the nearest yiOth of a foot, the depth of unsuitable material as road construction material and the depth of common material over rock to the nearest foot. The program permits four d i f f e r e n t ways of describing the t e r r a i n . The slope i s measured in percent from the center l i n e to the grade break or in percent from grade break to grade break (Figure 6 ) . Figure 6. Grade Breaks: V e r t i c a l Measurements The hor i z o n t a l distances are measured in a s i m i l a r way. I t i s the distance from a l l grade breaks to the center l i n e or between the grade breaks (Figure 7). Figure 7 . Grade Breaks: Horizontal Measurements Provision i s made in the program to read in up to eight grade breaks. The number of grade breaks read in to e i t h e r side of the center l i n e i s printed as a c o n t r o l on the l e f t hand side of a set of cross section f i e l d data. Then the program reads the accumulated chainage and elevation of the center l i n e at a cross section. Based on t h i s information, the program w i l l c a l c u l a t e the d i f f e r e n c e in elevation between the center l i n e and grade l i n e . The adjusted and unadjusted chainage and elevations with the number of a f f e c t i n g equations are printed out f o r c o n t r o l at every cross section set. For c a l c u l a t i o n s of the cross section area for cuts and f i l l s , the depth of unsuitable material i s deducted. I f there are chainage or elevation equations, the program w i l l adjust. VOLUME CALCULATION AND ALLOCATION The second program w i l l c a l c u l a t e the volumes. Basic input i s the standardized output from the previous program, dealing mainly with cross sectional data. Additional input describes the road standards themselves. The f i r s t set of input cards f i x e s the v e r t i c a l points of i n t e r s e c t i o n . The information required i s the elevation and chainage of the v e r t i c a l points of i n t e r s e c t i o n and the length of the v e r t i c a l curve. The program c a l c u l a t e s the dif f e r e n c e in elevation between the grade l i n e and center l i n e . The second set contains the design elements. The slopes are entered as the tangents and are separated f o r cut and f i l l slopes. For r e a l i s t i c volume c a l c u l a t i o n s , there i s a f a c i l i t y provided f o r shrinkage or compression of common material and swell of rock on f i l l s . Road C i s located on very steep h i l l s through rocky parts. Due to the steepness, i t i s assumed f o r volume c a l c u l a t i o n s , that loss of material and swell are equal. Shrinkage of common material i s 30 per-cent. For volume c a l c u l a t i o n s , the d i t c h width must be added to the subgrade width. The d i t c h volume i s not included i n these c a l c u l a t i o n s , because t h i s i s considered i n road construction as a separate operation and i s also accounted separately. The d i t c h width i s calculated based on the d i t c h slope and d i t c h depth. The s t a b i l i z e d subgrade width must be entered separately f o r the l e f t and r i g h t hand side of the grade l i n e . This provision takes widenings and turnouts into account, which are discussed i n previous chapters. The output of the volume c a l c u l a t i o n s i s s e l f explanatory with the provided headings (Appendix 2 ) . The f i r s t fourteen columns con-t a i n the de s c r i p t i o n of the road. It may be looked at as an echoprint f o r c o n t r o l purposes. Information about sidecast, the material used for f i l l from cut at a mixed p r o f i l e , i s of minor importance as input for the LP program, but required f o r the volume a l l o c a t i o n using the s t a t i o n -t o - s t a t i o n method. Of great i n t e r e s t i s the b a c k f i l l , the volume of gravel required between s t a t i o n s . This information contributes s i g n i f -i c a n t l y to the cost p r e d i c t i o n s , because gravel hauled over a long distance i s quite expensive. The net accumulated mass was a basic requirement f o r earth a l l o c a t i o n with the semi-graphical mass diagram. Using the LP technique f o r minimum earth a l l o c a t i o n cost, i n t e r e s t i s focussed on net volumes between stations as the constraints f o r volumes required ( f i l l ) or a v a i l a b l e ( c u t ) . Only the net masses and t h e i r location provide i n -formation about the distances over which the earth i s transported. The 360/67 IBM computer used f o r solving the LP model i s at the U n i v e r s i t y of B r i t i s h Columbia Computing Center. The system operates generally under the Michigan Terminal System (MTS). How-ever, the Mathematical Programming System (MPS), which solves the LP problem using the revised simplex method must run under IBM's Operating System (OS). Thus, three d i f f e r e n t systems are activ a t e d . MPS, s p e c i f i c a l l y set up for e f f i c i e n t processing of mathe-matical problems, i s a l i b r a r y program and con s i s t s of a compiler which processes the cont r o l language and sets up the c a l l s to sub-routines. Thus, the f i r s t step makes the system ready and the second step i s the executing one. An executor processes the subroutine c a l l s and reads the data. The job i s terminated by the executor by pro-ducing the r e s u l t s . Data for the LP Formulation Excavation i s the removal and r e l o c a t i o n of various types of earth and rock. The excavation costs are a function of s o i l type, earth moving equipment and transportation distance. Sometimes, there are separate cost classes f o r excavation, f o r rock and earth or common material ( R i t t e r and Paquette, 1967). I f the material can only be removed with b l a s t i n g or heavy r i p p i n g equipment, i t i s referred to as rock excavation. A l l other types of excavation are referred to as common excavation. Only one cost c l a s s f o r excavation i s considered f o r contracts in the U n i v e r s i t y of B r i t i s h Columbia Research Forest, and in accordance with t h i s p r a c t i c e , only one c l a s s i s considered i n the model. It i s anticipated that a D9 type c a t e r p i l l a r bulldozer w i l l be used for construction. Performance data were taken from C a t e r p i l l a r Tractor Company's "Fundamentals of Earthmoving" (1965) and are as follows: average speed - 2.4 mph i n f i r s t gear under st r e s s average speed - 6.5 mph i n t h i r d gear reverse empty push capacity with a U-blade 10.5 cubic yards e f f e c t i v e working time - 50 minutes per hour load f a c t o r f. = 0.7 (rock f. • 0.6, common material f - 0.8) fi x e d time i n c y c l e zero minutes, because there i s only hauling and returning time the hauling distance equals the return distance Computation of Excavation Cost The va r i a b l e time f o r one round t r i p i s calculated as follows: where t =» var i a b l e time of a cycle i n minutes d •= hauling distance i n feet s^ = hauling speed in mph s = return speed in mph f =» conversion f a c t o r f o r converting mph into feet per minute f «= 88 In t h i s equation, the variable time i s a l i n e a r function of speed and transportation distance. Therefore, the optimum freehaul distance i s a function of the maximum economic return time c y c l e . A cost analysis showed an optimal freehaul distance of 200 feet f o r rock and 400 feet f o r common ma t e r i a l . Dodic (1969) found good r e s u l t s i n assuming a freehaul distance of 300 feet independent of the material to be moved. Thus, the var i a b l e time i s cal c u l a t e d as follows: 300 300 t « + 24 • 88 6.5 • 88 300 + 300 t 211.2 572.0 t <= 1.94 minutes Production The hourly production depends on the blade capacity, the load f a c t o r and the number of hourly t r i p s . v = b • b c f where v <= bank cu yd per t r i p b Q <= blade capacity, 10.5 cu yd b^ <= load f a c t o r « 0.7 v - 10.5 • 0.7 7.35 cu yd per t r i p production: P t • v where p = production i n cu yd per hour t =• v a r i a b l e time per hour t «• e f f e c t i v e working time in minutes ef f v = bank cubic yards per t r i p 50 • 7.35 367.5 1.94 1.94 p » 189.43 cu yd per hour p » 190 cu yd per hour Hourly Rate of The D9 Operation The cost per hour f o r a D9 C a t e r p i l l a r was derived i n the following manner: cost (investment) of a D9 depreciation on a 1000 hour basis i n t e r e s t and insurance t o t a l owning cost $143,000.00 $ 14.30 per hour $ 4.72 per hour 19.02 per hour f u e l and l u b r i c a t i o n r e p a i r and labour t o t a l v a r i a b l e cost $ 3.79 per hour $ 12.87 per hour $ 16.66 per hour m a c h i n e r a t e $ 3 5 . 6 8 p e r h o u r p r o f i t 2 0 % $ 7 . 1 4 p e r h o u r o p e r a t o r i n c l u d i n g f r i n g e b e n e f i t s $ 6 . 0 0 p e r h o u r t o t a l h o u r l y c o s t f o r a D9 $ 4 8 . 8 2 T h i s c o s t c a l c u l a t i o n a p p l i e s t o a n e w b u l l d o z e r . O l d e r b u l l d o z e r s w i t h l e s s d e p r e c i a t i o n a r e r e n t e d t o g o v e r n m e n t a g e n c i e s a t $ 3 9 . 5 0 p e r h o u r ( F i n n i n g , p e r s o n a l c o m m u n i c a t i o n ) . B a s e d o n t h e f o r e g o i n g r e s u l t s , t h e e x c a v a t i o n c o s t a r e c a l c u l a t e d a s f o l l o w s : c = — V p w h e r e = e x c a v a t i o n c o s t p e r c u y d c n =• m a c h i n e r a t e pe r _ h o u r s i n d o l l a r s p «» p r o d u c t i o n p e r h o u r i n c u y d s 1 8 9 . 4 3 c v « $ 0 . 2 6 p e r c u y d These are the excavation cost plus transportation cost within freehaul distance. The average excavation cost w i l l be greater, except equal i n the case where no overhaul or borrow occurs. Haul Haul i s the product of volume and distance and i s divided into freehaul and overhaul. Within the freehaul, every cubic yard moved i s without an a d d i t i o n a l charge f or haul. There i s one u n i t p r i c e per unit volume moved. Obviously, increased freehaul increases the p r i c e f o r each unit volume moved. Overhaul i s the volume hauled i n excess of freehaul. The a d d i t i o n a l charge for volume transportation i s expressed in st a t i o n yards. Maximum overhaul distance i s a func-t i o n of earth moving production. The U. S. Forest Service (1970) found, based on a 100 yard freehaul distance, that the overhaul costs are an exponential function of the overhaul distance. However, in t h i s t h e s i s the overhaul costs are assumed to i n -crease l i n e a r l y with the distance. This has proved to be true f o r the U n i v e r s i t y of B r i t i s h Columbia Research Forest. The overhaul costs are ca l c u l a t e d as follows: where c Q = cost of overhaul in d o l l a r s per s t a t i o n per cu yd c m = machine rate per minute in d o l l a r s t = cycle time in minutes p = production per t r i p in cu yd c - $48.82 , 0.65 min ° 6o min 7.35 cu yd - 0.81 • 0.08 c - $0.07 o Obviously, there w i l l be a l i m i t to the-overhaul distance. This occurs, when the overhaul equals to the freehaul plus the quotient of borrow cost and overhaul cost. Borrow i s excavation outside the l i m i t s of the proposed road. Therefore, there are some addit i o n a l c l e a r i n g , grubbing and trans-portation cost to the excavation cost. Experience shows, that there i s a cost increase of 10% r e l a t i v e to the excavation cost f o r the U n i v e r s i t y of B r i t i s h Columbia Research Forest. c. = c + 0.1 • c b e e where c = borrow cost in d o l l a r s b c g = excavation cost in d o l l a r s c = $0.26 + $0.03 b c - $0.29 The maximum overhaul distance i s d - d + _JJ (Meyer, 1965) f c o where d = maximum overhaul i n feet d = maximum freehaul in feet f c = borrow cost i n d o l l a r s b c = overhaul cost i n d o l l a r s per s t a t i o n yard o A l l components are a v a i l a b l e i n order to c a l c u l a t e the maximum overhaul distance d = 300 + ^ ° 0.07 300 +403 d 8S 700 feet / o The maximum overhaul distance, interpreted in terms of d o l l a r s , means a maximum expenditure f o r excavation cost plus overhaul cost per cubic yard before borrowing. Excavation cost per cubic yard i s $0.26. At maximum economic overhaul distance the t o t a l cost i s $0.26 plus $0.07 per s t a t i o n yard times 4.03 st a t i o n s , or $0.55 per cubic yard. The 4.03 stati o n s are obtained by subtracting the freehaul distance from the maximum economic overhaul distance. Thus, i t i s cheaper to borrow at a cost of $0.29 per cubic yard within freehaul distance and to waste the excess cut than to pay more than $0.55 per cubic yard f o r excavation and overhaul. The sum of a l l costs r e l a t e d to earth moving costs are of three kinds: e i t h e r excavation, excavation and overhaul, and waste and borrow. VII. ANALYSIS OF EARTH ALLOCATION ANALYSIS OF THE MASS DIAGRAM The same road section as for the LP problem was analysed f or earth volume and d i s t r i b u t i o n using a mass diagram (Appendix 4). The freehaul i n both cases i s l a i d out i n order to maximize i t s d i s -tance and to minimize transportation and borrow. From the volume c a l c u l a t i o n s and the mass diagram the following r e s u l t s were obtained. There are 33,604 cu yd cut and 34,526 cu yd f i l l , which are the same qua n t i t i e s as in the LP model input. The borrow determined with the mass diagram i s 11,000 cu yd, the waste 10,000 cu yd. cut 33,604 cu yd $ 8,737.00 borrow 11,000 cu yd $ 3,190.00 excavation 44,604 cu yd $11,828.00 f i l l 34,526 cu yd waste 10.000 cu yd t o t a l f i l l 44,526 cu yd overhaul 17,300 Sti i yd $ 1,250.00 t o t a l cost $13,177.00 The d i f f e r e n c e between t o t a l excavation and t o t a l f i l l o r i g -inates from inaccuracies in the graph. However, more t r i a l s could improve the s o l u t i o n , but the e f f o r t would be greater than the benefit from the improved s o l u t i o n . The t o t a l overhaul equals to 17,300 sta yd at $0.07 per s t a t i o n yard. Therefore, the trans-portation cost are $1,250.00. ANALYSIS OF LINEAR PROGRAMMING SOLUTION Ite r a t i o n s The optimal solution was found a f t e r 161 i t e r a t i o n s (Appendix 3). The smallest improvement of the function value due to any i t e r a t i o n was $0.06 at the least . i t took the computer 0.65 seconds to perform a l l i t e r a t i o n s of the 68 by 418 matrix; thus, the time needed f o r c a l c u l a t i n g one i t e r a t i o n takes approximately .0025 seconds. One hour of ce n t r a l processing u n i t (CPU) time costs at t h i s computer (IBM 360/67) $250.00, or per second $0.07. Therefore, the i t e r a t i o n s were j u s t i f i e d , because the lower function value was greater than the cost of the i t e r a t i o n . However, i t i s desi r a b l e to terminate the i t e r a t i o n s , i f the improvement of the objective function i s l e s s than a s p e c i f i e d amount. This s p e c i f i e d amount could be f o r instance the computing cost per i t e r a t i o n or any other c r i t e r i a chosen by the programmer. The optimum volume a l l o c a t i o n i s printed as output i n Appendix 3. However, the "A" in column 1 indicates, that there are alternate s o l u t i o n s . Earth Moving S t a t i s t i c s Obtained by Linear Programming Given the net volumes at a p a r t i c u l a r s t a t i o n , optimum earth a l l o c a t i o n i s reached a f t e r 33,604 cubic yards of excavation and 10,538 cubic yards borrowed. This adds up to a t o t a l excavation of 43,220 cubic yards. The volume i s allocated to f i l l with 34,526 cubic yards and 9,616 cubic yards were wasted. These s t a t i s t i c s are summarized in the following table: cut 33,604 cubic yards $ 8,737.00 borrow 10,538 cubic yards $ 3,056.00 excavation 44,142 cubic yards $11,793.00 f i l l 34,526 cubic yards waste 9,616 cubic yards t o t a l f i l l 44,142 cubic yards Minimum Earth Moving Cost The minimum earth moving cost i s the value of the objec t i v e function a f t e r the f i n a l i t e r a t i o n . T h i s value i s given i n Appendix 3. The cut, borrow, and minimum earth moving cost f o r the excavation and moving of 44,142 cu yd to f i l l s t a t i o n s was $13,003.73. The average excavation and moving costs per cubic yard are $0.29. TOTAL COSTS: MASS DIAGRAM VERSUS LINEAR PROGRAMMING The t o t a l costs include earth moving and o f f i c e work i n planning the earth moving. A summary of these t o t a l costs i s shown in the following Figure 8: mass diagram L P - a l l o c a t i o n savings by LP cut 8,737.00 8,737.00 -borrow 3,190.00 3,056.00 134.00 earth a l l o c a t i o n 1,250.00 1,210.00 40.00 t o t a l fieldwork cost 'SS SCSS3 tSSffl E 3 CB I S C 3 S S S S E3SSCS 13,177.00 B o a s o g e a B m o e t s s u a e a B a : 13,003.00 174.00 Figure 8. Summary of To t a l Earth A l l o c a t i o n Cost ,. .,„.___,„ ... mass diagram L P - a l i o c a t i o n savings by LP cost of c a l c u l a t i o n s f o r input - 70.00 -70.00 data processing cost B s s a a a a s s s s s s s & S H S P a s s a s o f f i c e work cost SBSasssSBsaissssiasssscassssssasEsssss t o t a l cost 20.00 ssssssmeaa esses assessesxsi 20.00 13,197.00 40.00 110.00 13,113.00 -20.00 Z&3S3S3CSS3S3&ISBC1 S S S M S S S St £3 -90.00 84.00 Figure 8. Summary of To t a l Earth A l l o c a t i o n Cost The costs of cut are equal f o r both approaches, because the cost c a l c u l a t i o n s are based on the same volume c a l c u l a t i o n s . The cost d i f f e r e n c e f o r borrow i s due to non optimal a l l o c a t i o n of cuts to f i l l s by the mass diagram, and graphical e r r o r s . The overhaul costs obtained by LP are true overhaul costs, because these are calculated by hand f o r moving one cubic yard from c u t s s t a t i o n i to f i l l s t a t i o n j , where the f i l l s t a t i o n s are located within maximum economic overhaul distance from cut s t a t i o n i . These c a l c u l a t i o n s and the coding cost $70.00. The freehaul distance f o r the mass diagram i s s i m p l i f i e d and drawn in the graph as the distance from one volume balance point to the next. The saving thus obtained by LP due to greater p r e c i s i o n i s $40.00, which w i l l increase with the number of freehauls in the mass diagram. The saving by using LP i s $174.00 for earth moving, where the o f f i c e work i s $90.00 more expensive than f o r the mass diagram. I t can be seen from the t o t a l costs obtained by the mass diagram and LP, that the LP solution y i e l d s a t o t a l saving of $84.00 or 0.6% of the earth moving and planning costs based on the mass diagram. VIII. SUMMARY AND CONCLUSION The purpose of the th e s i s i s a comparative study of earth-work cost. Earthwork costs are obtained by the t r a d i t i o n a l mass diagram method and the new LP technique. The new approach with the LP technique i s explained i n d e t a i l . The same basic data are used f o r both methods for v a l i d comparison, p a r t i c u l a r l y the concept of freehaul and overhaul f o r cost c a l c u l a t i o n s . The LP solution i s known to y i e l d the optimum due to the proof of o p t i m a l i t y f o r the revised simplex method which was used in the MPS l i b r a r y program. I t i s known, that the earthwork and i t s asso-c i a t e d cost obtained by the mass diagram are not optimal due to graphical inaccuracies and s i m p l i f i c a t i o n s , but the extent of the deviation from the optimal r e s u l t i s not known. No s i g n i f i c a n t d i f f e r e n c e i n eit h e r earthwork volume or earth-work cost i s found. The e x i s t i n g d i f f e r e n c e between the r e s u l t s obtained are p a r t l y due to the graphical solution procedure of the mass diagram, and p a r t l y to a di f f e r e n c e in freehaul. The freehaul distance i s used in the LP model according to the d e f i n i t i o n , whereas the freehaul distance i n the mass diagram i s taken, f o r reasons of s i m p l i c i t y in drawing, as the distance between volume balance points. The same i s true f o r the overhaul distance. The earthwork cost ob-tained with the mass diagram w i l l deviate more from the true cost, as determined from the LP model, the greater the haul in st a t i o n yards. There are many alternative solutions in the LP solution due to the freehaul, where every cubic yard moved costs the same amount independent of the transportation distance. This is not true in practice and there are two ways to overcome this disadvantage. If the distance, for some reason, must s t i l l be partitioned into free-haul and overhaul, each cubic yard moved within freehaul distance should be penalized on a foot-yard basis. The penalty must be ex-tremely small, so that it does not change the functional value; a value added could be in the order of $0.0001 per foot yard. The second possibility is to disregard freehaul and calculate the excavation cost and add to each station a station yard cost. The earth moving costs calculated are closer to the existing condi-tions with the latter system, rather than separating freehaul and overhaul distances with freehaul penalties. An LP formulation in-cluding the excavation cost only plus the station yard cost will give a greatly improved result in the accuracy of earthwork cost compared with the results obtained by the mass diagram analysis. IX. SUGGESTIONS FOR FURTHER RESEARCH The r e s u l t s obtained by the LP technique are c l o s e r to the r e a l conditions than the r e s u l t s obtained by the mass diagram. The diff e r e n c e increases, as the overhaul becomes greater. Therefore, the LP formulation of the problem i s v a l i d and further research i s j u s t i f i e d . However, the tedius c a l c u l a t i o n s f o r the mass d i s t r i b u t i o n are not excluded f o r eit h e r a l l o c a t i o n method and only the earth a l l o c a t i o n cost i s minimized. Therefore, the problem of minimizing excavation cost due to road lay-out should be studied i n greater d e t a i l . An attempt was made by Lloyd and Sharpels (1969). The choice of the lo c a t i o n of a grade l i n e becomes a sequential decision process, f o r which s o l u t i o n by the dynamic programming (DP) technique (Bellman, 1957; Bellman and Dreyfus, 1962),is the most s u i t a b l e . Use of the DP part of the model would minimize the excavation cost and the LP part minimizes a l l o c a t i o n cost. The combined model using DP and LP would minimize t o t a l earthwork cost on a road. Adamovich, L., and Webster, J . B. 1968. Road Location and Construction in the U. B. C. Research Forest Area. The Truck Logger. 24(4). 6 pp. Adamovich, L. 1970. Lectures in Forestry 463, Forest Transportation Systems. U n i v e r s i t y of B r i t i s h Columbia, Faculty of Forestry. Bellman, R. 1957. Dynamic Programming. Princeton U n i v e r s i t y Press, Princeton, New Jersey. 342 pp. Bellman, R., and Dreyfus, S. E. 1962. Applied Dynamic Programming. Princeton U n i v e r s i t y Press, Princeton, New Jersey. 363 pp. Boughton, W. C. 1966. Planning the Construction of Forest Roads by Linear Programming. Aus t r a l i a n Forestry. 31(2):111-120. Byrne, J . J . , and Googins, P. H. 1960. Logging Road Handbook. U. S. Department of A g r i c u l t u r e , Forest Service, Handbook Number 183. 65 pp. Capper, P. L., and Cassie, W. F. 1963. The Mechanics of Engineering S o i l s . Spon, London. 298 pp. C a t e r p i l l a r T ractor. 1965. Fundamentals of Earthmoving. 81 pp. Dantzig, G. B. 1963. Linear Programming and Extensions. Princeton U n i v e r s i t y Press, Princeton, New Jersey. 632 pp. Dodic, D. 1969. Optimum Construction Organization f o r Road K in the U n i v e r s i t y of B r i t i s h Columbia Research Forest. Report For 563. 43 pp. Edwards, H. M . , and Townsend, D. L. 1961. General Aspects of Haul Road Construction. Pulp and Paper Magazine of Canada. 62(2):153-170. Finning Tractor & Equipment Co. L t d . , 555 Great Northern Way, Vancouver BC. 1970. Personal communication. H i l l i e r , F. S., and Lieberman, G. J . 1968. Introduction to Operations Research. Holden-Day Inc., San Francisco. 638 pp. Sharpels, T., and Lloyd, D. 1969. A Computer Approach to Main Haul Road Design. B. S. F. Thesis. Faculty of Forestry, U n i v e r s i t y of B r i t i s h Columbia, Vancouver. 40 pp. Manual of Geometric Design Standards f o r Canadian Roads and Streets. 1967. Canadian Good Roads Association, Ottawa. 208 pp. Meyer, C. F. 1967. Route Surveying. International Textbook Company, Scanton. 671 pp. P i e r c e , J . K. 1964. Forest Engineering Handbook. U. S. Department of the I n t e r i o r , Bureau of Land Management. Oregon State O f f i c e P u b l i c a t i o n . 220 pp. R i t t e r , L. J . , and Paquette, R. J . 1967. Highway Engineering. Ronald Press Company, New York. 782 pp. Simonnard, M. 1966. Linear Programming. Prentice H a l l Inc., Englewood C l i f f s . 121 pp. Smythe, W. R., and Johnson, L. A. 1966 Introduction to Linear Programming. Prentice H a l l Inc., Englewood C l i f f s . 121 pp. United States, Department of the I n t e r i o r , Bureau of Land Management. 1970. Logging, Transportation and Contractual Costs, Schedule 16. Portland Service Center, Portland. Waelti, H. 1960. Die Planung und Projektierung von Waldaufschiies-sungsanlagen in B r i t i s c h Kolumbien. Schweizerische Z e i t s c h r i f t fuer Forstwesen. 111(9/10):488-507. Waelti, H, Manager, Forest Engineering D i v i s i o n , B r i t i s h Columbia Forest Service, V i c t o r i a BC. 1970. Personal communication. CHAIN EG COR CHG GND ELV Q COR ELV 8 SETS' OF ELEV + DISTANCES - LEFT SIDE - TOP ROW,RIGHT SIDE - BOTTOM ROW 1 ELEV ID 1ST 2ELEV 2DIST 3 ELEV 3DIST 4ELE V 40 I ST 5ELE V 501 ST 6ELEV 6DIST 7ELEV 7DIST 8ELEV 8DI ) 0 . 1 0 . 500.0 1 500. C 499. 5 0 499. 5 15G 0. 0 c 0. G 0 0.0 0 0.0 0 0.0 0 0.0 0 1 49 9.5 0 499.5 150 .0. 0 0 0.0 0 0. 0 0 0. 0 0 0.0 0 0.0 0 NCBSL= 2 NOB SR = 2 SOIL — C O O 100. 1 100. 507. 0 1 507. 0 506. 5 0 529. 0 150 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 0. 0 0 506. 5 0 506.5 150 0. 0 0 • 0. 0 0 0. 0 0 0.0 0 0 .0 0 o . o 0 NOB SL = 2 NOB SR = 2 SOI L 0 0 G —J 200. 1 200. 517. 0 1 517.0 516.5 0 524.0 150 0.0 0 0.0 0 0.0 0 0. G 0 0. 0 0 0. c 0 516. 5 C 50 1. 5 150 0. 0 0 0. 0 0 0.0 0 0 .0 0 0.0 0 0.0 0 NCBSL = 2 NOBSR= 2 SOIL = 0 0 0 300. 1 300. 522. 0 1 522 . 0 521 . 5 0 529.0 150 0 .0 0 0.0 0 0. 0 0 0. G 0 0. 0 0 0.0 0 521. 5 0 506. 5 150 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 0. 0 0 N G B S L = 2 NOBSR= 2 s e n 0 0 0 350. 1 350. 526.4 1 526 .4 525 .9 0 525.9 150 0.0 0 0. 0 G 0. G 0 0.0 0 0.0 0 0.0 0 525. 9 0 525.9 150 0.0 0 0.0 0 0.0 0 0. 0 0 0. 0 0 0. 0 0 NCBSL= 2 NOBSR= 2 SOIL = G O O 400. 1 400 . 531.0 1 531 .0 530. 5 0 523.0 15C 0. 0 0 0. 0 0 0. 0 0 0.0 0 0.0 0 0.0 0 530.5 0 538.0 150 0 .0 0 0.0 0 0. 0 0 0.0 0 0.0 0 0.0 0 NOBSL= 2 NOBSR= 2 SOIL = 0 0 0 • 500 . 1 500 . 529.0 1 529. 0 528. 5 G 500. 0 150 0. 0 0 0.0 0 0.0 0 0 .0 0 0.0 0 0. G 0 528 .5 0 546. 5 150 0. 0 0 0. 0 c 0. 0 0 0. 0 0 0.0 0 0.0 0 NOBSL= 2 NOB SR = 2 SOIL = G O O 5 50. 1 550. 534. 2 1 534. 2 53 3. 7 0 488. 7 150 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 G. C 0 533. 7 0 548. 7 150 0. 0 0 0. 0 0 0.0 0 0.0 0.0 0 0.0 0 NOB SL = 2 NOBSR= 2 SGI L = 0 0 0 CHAIN EC COR CHG GNC ELV Q COR ELV 8 SETS OF EL EV + DISTANCES - LEFT SIDE - TOP ROW,RIGHT SIDE - BOTTOM ROW 1ELEV 1DIST 2ELEV 2D I ST 3ELEV 3D I ST 4ELEV 4DIST 5ELEV 5DIST 6 EL EV 6DIST 7 EL EV 7DIST 8ELEV 8DI 600. 1 600. 540.C 1 NOBSL= 2 N08SR= 2 SOIL 54 0. C 0 0 0_ 53 9.5 539. 5 0 0 509.5 150 554.5 150 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0. G 0.0 0 0 0. 0 0.0 0 0 C. G 0.0 0 0 700. 1 7 00. 555.0 1 Jtt£BJSJ^=L_2 NOBSR ~ 2 SCIL 555.0 O O P 554.5 554. 5 0 C 517.0 150 592.0 150 0 .0 0. 0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 0. c 0.0 0 0 0. 0 0.0 0 0 0.0 0. 0 0 0 800. 1 800. 562.0 1 N C B S L = 2 NCBSR= 2 SOIL 562 .0 O O P 56 1.5 561.5 0 0 546.5 150 591.5 150 0. 0 0.0 0 0 0.0 0.0 C 0 0. 0 0.0 0 0 0. 0 0. 0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 850. 1 850. 560 .2 1 560. 2 NGBSL= ? NOBSR= 2 SOIL = O O P 559.7 55 9.7 0 0 5 2 9.7 150 604.7 150 0. 0 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 0.0 0.0 0 0 0 .0 0.0 0 0 0.0 0. 0 0 0 900. 1 900 NOESL= 2 NOBSR: 559.G 1 559.0 2 SOIL = O O P 558.5 558.5 0 P 513.5 150 611.0 150 0. 0 0.0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0. C 0.0 0 0 1000. 1 1000. NOBSL= 2 NOB SR-557.0 1 557.0 ! SOIL = G O G 556. 5 55 6.5 0 0 511.5 150 616.5 150 0.0 C. 0 0 0 0.0 0. C 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 1100. 1 1100. 552. 5 1 552. 5 NCBSL= 2 NCBSR= 2 SOIL = O O P 552. 0 55 2. 0 P 0 4-99.5 150 604.5 150 0.0 0. 0 0 0 0.0 0. 0 0 0 0 .0 0.0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 120C. 1 1200. 547.0 1 547.0 546.5 546. 5 0 0 509.0 150 576.5 150 0.0 0. 0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 0.0 0. 0 0 0 CHAIN EQ COR CFG GNC ELV C COR ELV 8 SETS OF ELEV + DISTANCES - LEFT SIDE - TOP ROW,RIGHT SIDE - BOTTOM ROW IE LE V 1DI ST 2ELEV 2DIST 3ELEV 3DIST 4-ELEV 4C 1ST 5ELEV 5 CIST 6 EL EV 60 1ST 7 ELEV 7DIST 8E LEV 8DI ) 13 00. .1 1.3 00. 542 .0 1 542 .0 541.5 0 481 .5 150 0.0 0 0.0 c 0. c 0 0. C 0 0. 0 0 0.0 0 \ 541. 5 0 571. 5 150 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 0. 0 0 NCBSL= 2 NOBSR- 2 SCIL = 0 0 0 1320. 1 1320. 540.6 x 540.6 540. 1 0 480. 1 150 0. 0 c 0. 0 0 0. 0 0 0.0 0 0.0 0 0.0 0 540.1 0 577.6 150 0 .0 0 0.0 0 0.0 0 0. 0 0 0. 0 0 0. 0 0 NCBSL= 2 NOBSR= 2 SOIL = 0 0 0 1367. 1 1367 . 538 .0 1 538.0 5 3 7.5 0 507. 5 150 0. 0 0 0. 0 0 0.0 0 0.0 0 0 .0 0 0.0 0 537.5 0 567.5 150 0.0 0 0.0 0 0. 0 0 0. 0 0 0.0 0 0.0 0 N08SL= 2 NOBSR= 2 SOIL = 0 0 0 1400 . 1 1400 . 535.0 1 535. 0 534. 5 0 497. 0 150 0. 0 0 0.0 0 0.0 0 0.0 0 0.0 0 0. c 0 534.5 0 56 4.5 150 0. 0 0 0. 0 0 0. 0 0 0.0 0 0.0 0 0.0 0 NOBSL= 7 NOB SR = 2 SOIL 0 0 0 1500. 1 1500. 566. 0 1 566. 0 565. 5 0 535. 5 150 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 0. 0 0 565. 5 0 618. 0 15 0 0. 0 0 0. 0 0 0.0 0 0.0 0 0 .0 0 0.0 0 NOB SL = 2 NOB SR = 2 SCIL = 0 0 0 1573. 1 1573. 57 0. 0 1 570. 0 569.5 0 539.5 150 0 .0 0 0.0 0 0.0 0 0. 0 0 0. 0 0 0. 0 0 569, 5 0 607. G 150 0. 0 0 0. 0 0 0.0 0 0.0 0 0.0 0 0.0 0 NCBSL= 2 NGBSR= 2 SOIL = 0 0 0 1600. 1 1 600. 568 .0 1 568 .0 567.5 0 537.5 150 0.0 0 0.0 0 0. 0 0 0. 0 0 0.0 0 0.0 0 567. 5 0 620. 0 15 0 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 0. 0 0 NOBSL= 2 NOBSR= 2 SOIL .= 0 0 0 1634. 1 1634. 567.0 1 567.0 566 ,5 0 551.5 150 0. 0 0 0. 0 0 0. 0 0 0. 0 0 0.0 0 0.0 0 566.5 0 634.0 150 0.0 0 0.0 0 0.0 0 0.0 0 0. 0 0 0. 0 0 NCBSL= 2 N G B S R = 2 SjQJL = 0 0 0 C H A I N EG COR CHG GNC ELV Q COR ELV 8 S E T S OF E L E V + D I S T A N C E S - L E F T S I D E - TOP ROW,RIGHT S I D E - BOTTOM ROW 1 E L E V 1 D I S T 2 E L E V 2D 1ST 3 E L E V 3 D1ST 4 E L E V 4 D I S T 5 E L E V 5 D I S T 6 E L E V 6 0 I S T 7 E L E V 7 D I S T 8 E L E V 8 D I 1 7 0 0 . NOBSL = .1 2 1 7 0 0 . NOfiSR= 550 .0 2 _ S H I L 1 5 5 0 . 0 0 0 0 549 . 5 5 4 9 . 5 0 0 5 1 9 . 5 6 0 9 .5 1 5 0 150 0.0 0 .0 c 0 . 0. 0 ;. 0.0 C 0 0. 0 0.0 0 0 0.0 0. G 0 0 0.0 0. 0 0 0 0.0 0. 0 0 ^ 0 1 8 0 0 . .J.C.B.S.L= 1 2 18 0 0 . _NOBSB = 52 5.0 2_SQ_I L_ 1 5 2 5 . 0 G O O 5 2 4 . 5 5 2 4 . 5 0 0 5 1 7 . 0 5 6 3 . 5 150 1 5 0 0. 0 0.0 0 0 ; 0.0 i o. o 1 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0.0 0 0 1 i 1 8 3 1 . NOBSL= 1 2 1 8 3 1 . NOB SR = 5 2 3 . 0 2 SOI L 1 5 2 3 . 0 C O O 5 2 2 . 5 5 2 2 . 5 0 0 5 1 5 . 0 5 3 7 . 5 1 5 0 150 0.0 0. 0 0 0 ' S 0 .0 / 0. 0 \ . 0 G 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 o.o 0 0 0. 0 0.0 0 0 \ ( I 1 8 9 0 . N.CB.S.L.JL 1 2 1 8 9 0 . NCBSR= 5 4 0 . 0 2 _ S H I L 1 5 4 0 . C 0 0 0 5 3 9 . 5 5 3 9 . 5 0 0 5 3 2 . 0 5 3 9 . 5 150 1.50 0.0 C. G 0 0 0.(0 0.)0 , 1 ' 0 0 0.0 0.0 0 0 0. c 0.0 0 0 0. 0 0.0 0 0 0. c 0.0 0 0 / 1 \ 1 9 0 0 . N OBSL-1 2 1 9 0 0 . NOBSR= 5 4 1 . 4 2 S O I L 1 5 4 1 . 4 0 0 0 5 4 0 . 9 5 4 0 . 9 0 0 5 4 0 . 9 5 4 0 . 9 1 5 0 1 5 0 0 .0 0. 0 0 0 o. (!) o.6\ \ 0 0 0. 0 0.0 0 0 0.0 0.0 0 0 0.0 0.0 0 0 0.0 0. 0 0 0 \ \ ) 2 0 G 0 . Nr.BSL = 1 2 2 0 0 0 . NOBSR= 5 6 1 . 0 2 SO II 1 5 6 1 .0 0 0 0 5 6 0 . 5 5 6 0 . 5 0 0 5 3 0 . 5 5 6 0 . 5 150 1 5 0 0. 0 0.0 0 0 0.0 t 0.0 1 G 0 ) -0. 0 0.0 0 0 0. 0 0.0 0 0 0.0 o. 0 0 0 0.0 0. 0 0 0 1 2 1 0 0 . NOBSL= 1 2 21 00 . NOBSR= 577 .0 2 S O I L 1 5 7 7 . 0 0 0 0 5 7 6 . 5 5 7 6 . 5 0 0 5 7 6 . 5 5 6 9 . 0 15G 150 0. 0 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 0.0 0. 0 o 1 0 0.0 0. 0 0 0 0.0 ,0 \ 0 0 0 2 2 0 0 . NGBSL= 1 2 2 0 0 . 2 &L0BSR = 5 9 0 . 0 2L_S0IL 1 5 9 0 . C 0 0 0 5 8 9 . 5 5 8 9 . 5 0 0 5 8 9 . 5 589 .5 150 150 0. 0 0.0 c 0 0. 0 0. G 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0.0 0 0 CHAIN EQ COR CHG GND ELV Q COR ELV 8 SETS OF ELEV + DISTANCES - LEFT SIDE - TOP ROW,RIGHT SIDE - BOTTOM ROW 1ELEV 1DIST 2ELEV 2D 1ST 3E L EV 3DIST 4ELEV 4DIST 5ELEV 5DIST 6ELEV 60IST 7ELEV 7DIST 8ELEV 8DI 2370. 1 NOBSL= 2 2370. NOB SR= 609.0 1 2 SOIL 609.0 G O O 608.5 608.5 0 0 601,0 15 0 631.0 150 0.0 0.0 C 0 0.0 0. 0 0 0 0 .0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0.0 < 2470. 1 NOB SL: 2470. 631.0 1 631. 0 N0BSR= 2 SOIL = 0 0 0 630. 5 630.5 0 C 623.0 150 608.0 150 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 G. 0 0 0 0,0 0.0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 2515. 1 2515. 628. 0 1 628. 0 627.5 0 612.5 150 0 .0 0 0.0 0 627. 5 0 612. 5 150 0. 0 G 0.0 0 NOB S L - 2 N0BSR= 2 SOIL = O O P  0.0 0.0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 0. 0 o.c 0 0 2570. 1 2570. 631.0 1 631.0 630.5 0 638.0 150 6 3 0. 5 0 63 8. 0 15 0 NOB SL= 2 NCBSR~ 2 SCIL •= O O P 0.0 0.0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 0.0 0.0 0 0 0.0 0. 0 0 0 2670. 1 2.670, 642 .5 1 642.5 642.0 0 634. 5 150 O.G 0 0. 0 0 0.0 642.0 0 664.5 150 0.0 0 0.0 0 0.0 NOBSL= 2 NOBSR= 2 SOIL = 0 0 0  0 0 0. 0 0. G 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 2770. 1 2770. 657.0 1 657.0 NOBSL= 2 NOBSR= 2 SOIL = G O O 656. 5 6 5 6.5 0 0 626.5 150 694.0 150 0. 0 0.0 0 0 0. 0 0. 0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0.0 0 0 2870. 1 2870. 660.0 1 660. 0 NOBSL= 2 NOB SR= 2 SOIL = O O P 659. 5 659.5 0 0 592.0 150 704.5 150 0. 0 0. 0 0 0 0.0 0. 0 0 C 0.0 0. 0 0 0 0 .0 0. 0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 2877. 1 2877. 659.1 1 659.1 CHAIN EG COR CHG GND ELV G COR ELV 8 SETS OF ELEV + DISTANCES - LEFT SIDE - TOP ROW,RIGHT SIDE - BOTTOM ROW 1ELEV 1DIST 2ELEV 201 ST 3ELEV 3D I ST 4ELEV 401 ST 5ELEV 5DIST 6ELEV 6 D 1ST 7 EL EV 701ST 8ELEV 8DI 295 2. 1 2 9 52. JiDiisL^2___jmfimE^^__jscm_ 650. 0 1 650.0 649.5 0 634.5 150 0.0 0 0.0 0 0.0 0 0.0 G 0.0 0 O.G 0 649. 5 0 664. 5 15G C O 0 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 O O P __ 2970. 1 2970. 650. 0 1 J^j0flSX^_2_!mBJSR^___2._S_C_IJ, 650. 0 0 0 0 649, 5 649. 5 0 G 634.5 150 664.5 150 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0.0 0 0 0.0 0 .0 0 0 0. 0 0.0 0 0 0. 0 0. 0 0 0 3G7C. 1 NOBS L-3070. N 0 B S R -65 8.0 1 658 .0 2 SOIL = O O P 6 57 .5 657. 5 0 0 6 20.0 150 6 80.0 150 0. 0 0.0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 3124. 1 3124. 658.0 1 658.0 -N0JiSJ-iL_2 JiPiaSRiE 2_S.G.U,__H 0_0__Q_. 657. 5 657. 5 0 0 627.5 150 672.5 150 0.0 0.0 0 0 0. G 0.0 0 0 0. 0 O.G 0 0 0.0 0.0 0 0 0 .0 0. 0 0 0 0.0 0. 0 0 0 3170. 1 3170. 654.0 1 654.0 NOBSL- 2 N0BSR= 2 SOIL = O O P 6 53. 5 65 3.5 0 0 60 8. 5 150 706.0 150 0. 0 0.0 0 0 0. 0 O.G 0 0 0.0 0. 0 0 0 0 .0 0. 0 0 0 0.0 0.0 0 0 0.0 0 0.0 0 3240. 1 3240 . 656.5 1 6 5 6 . 5 _N0.8..SLiL...2 NCB.S8 = 2.. SC.LL...= C O 0 656. 0 656.0 0 0 633.5 150 686.0 150 0.0 0. 0 0 0 0.0 0. 0 0 G 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 o.o 0 0 0. 0 0.0 0 0 3270. 1 3270. 658. 0 1 658. 0 6 5 7 . 5 0 627.5 150 0.0 0 0 .0 0 0.0 0 0. 0 0 0. 0 0 O.G 0 657. 5 0 665. 0 15G 0. 0 0 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 NGB S L = 2 N G B S R = 2 SOIL = O O P . . NCBSL= 2 NOBSR= 2_SJLU_ THESIS PROJECT, UNIVERSITY OF BRITISH COLUMBIA, RESEARCH FOREST, ROAD C, 1 9 7 G P A G E 7 ^ CHAIN EG COR CHG GND ELV G COR ELV 8 SETS OF ELEV + DISTANCES - LEFT SIDE - TOP ROW,RIGHT SIDE - BOTTOM ROW t 1ELEV 1 D I S T 2ELEV 2DIST 3ELEV 30IST 4ELEV 4DIST 5 ELEV 5 D1ST 6ELEV 6 0 I S T 7ELEV 70 1 ST 8ELEV 8DI < !3 7G. 1 33 70. 6 84.0 1 NGBSL= 2 NOBSR= 2 S C I L 684.0 O O P 68 3.5 683. 5 0 0 646.0 150 698.5 150 0 .0 0.0 0 0 0.0 0.0 G 0 0. 0 0.0 0 0 0. 0 0.0 G 0 0.0 0.0 0 0 0.0 0. 0 3470. 1 3 4 7 0 . 700.0 1 700.0 N 0 B S L = 2 NOBSR= 2 SOIL = C O O 699 .5 699. 5 0 0 654.5 150 737.0 150 0. 0 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 0. 0 0. 0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 3570. 1 NOBSL" 35 70 . NOBSR-695.0 1 695.0 694, 5 694. 5 0 0 649.5 150 709.5 150 0. 0 0.0 0 0 0. 0 0.0 0 0 0.0 0. 0 0 0 0 .0 0. 0 0 0 0 .0 0.0 0 0 0.0 0.0 0 0 2 SOIL = C O O 3 6 7 0 . 1 3670. 715.0 1 715.0 NQBSL= 2 NQBSR= 2 SOIL = O O P 714.5 714.5 0 0 662.0 150 759.5 150 0. 0 0. 0 0 0 0. 0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0.0 0 0 0. 0 0.0 0 0 3770. 1 3770. 722.0 1 722.0 NOBSL= 2 NOBSR= 2 SOIL = O O P 721. 5 721. 5 0 0 684.0 150 759. 0 150 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0.0 0 0 0.0 0 .0 0 0 0. G 0.0 0 0 3779. 1 3779. 723. 0 1 J±C8ALLL__2 _QB_S_ 2__LLL_ 123. 0 O O P 72 2. 5 722.5 0 0 677.5 150 752. 5 150 0 .0 0. 0 0 0 0.0 0. 0 0 0 0. G 0.0 G 0 0.0 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 3870. 1 3870. 726 .0 1 726.0 725.5 0 710.5 15G O.C 0 0.0 0 0. G 0 0. 0 0 0.0 0 0.0 0 725. 5 0 718. 0 150 . 0.0 0 0.0 0 0.0 0 0.0 0 0.0 0 0. 0 0 NCBSL= 2 NGBSR= 2 ' S C I L = O O P . CHAIN E C C O R CHG GND ELV Q C O R ELV 8 SETS OF ELEV + DISTANCES - LEFT SIDE - TOP ROW,RIGHT S IDE - BOTTOM ROW 1ELEV 1DIST 2 ELEV 2 DIST 3ELEV 3D 1ST 4ELEV 4DIST 5ELEV 5DIST 6ELEV 6DIST 7ELEV 7DIST 8ELEV 8DI 4 0 7 0 . 1 4 0 7 0 . 7 4 7 . 5 1 NGBSL- 2 NOBSR= 2 SOIL 7 4 7 . 5 G O O 7 4 7 . 0 74 7. 0 0 0 7 6 9 . 5 150 762 .0 150 0.0 0.0 0 0 0. G 0 . 0 G 0 0. 0 0. 0 G 0 0 . 0 0 . 0 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 4 1 7 0 . 1 4170 . 7 5 7 . 0 1 757.G NOBSL= 2 NOBSR- 2 SOIL = O O P 756 . 5 75 6.5 P 0 7 3 4 . 0 150 77 1.5 150 0. G 0 . 0 0 0 0 . 0 O.G 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 .0 0 . 0 0 0 4 2 7 0 . 1 4270 7 6 1 . 0 1 NOB S L - 2 NOBSR= 2 SOIL 761.0 C O O 760. 5 7 6 0 . 5 0 0 6 9 3 . 0 150 8 2 0 . 5 150 0.0 0. G 0 G 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 . 0 0 0 7 6 4 . 0 1 164.C SJJL^E 0 ..0..0„_ 763 . 5 763 . 5 0 G 6 8 1 . 0 150 786. 0 150 0 . 0 0. 0 • 0 0 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 . 0 0 0 0. G 0 . 0 0 0 4370. 1 4 3 7 0 . 767. 0 1 767 .0 N O B S L = 2 NOBSR- 2 S0 I L = O O P 7 6 6 . 5 766. 5 P G 6 6 1 . 5 150 826. 5 150 0 .0 0. 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0 . 0 0. 0 0 0 4 4 2 0 . 1 4 4 2 0 . 7 7 8 . 6 1 778 .6 j*JCB.SJ_=_2 N.0.8_S.B= 2.._SJUL.._5 Q._.0._0._ 778 . 1 778 . 1 0 0 7 2 5 . 6 150 838.1 150 0. 0 0 . 0 C 0 0 . 0 0 . 0 0 0 0. G 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 4 4 7 0 . 1 4 4 7 0 . 79 1,0 1 7 9 1 . 0 NGPSL- 2 NOBSR- 2 SOIL = O O P 7 9 0 . 5 7 9 0 . 5 0 0 7 3 8 . 0 150 8 2 8 . 0 150 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 .0 0. 0 0 0 0 . 0 0. 0 0 0 4 5 7 0 . 1 4 5 7 0 . 8 0 3 . 0 1 803 .0 802 . 5 802 .5 0 0 750. 0 150 8 3 2 . 5 150 0. 0 0 . 0 0 0 0 . 0 0. G 0 0 0 . 0 0 .0 0 0 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 CHAIN EQ COR CHG GND ELV Q COR ELV' 8 SETS OF ELEV + DISTANCES - L E F T S IDE - TOP ROW,RIGHT SIDE - BOTTOM ROW 1ELEV 1DIST 2ELEV 2D 1ST 3ELEV 3DIST 4ELEV 401 ST 5ELEV 501 ST 6ELEV 6 DI ST 7ELEV 7DIST 8ELEV 8DI 4 6 7 0 . .1 jmBSJli 46 70 . NOB SR~ 820 .G 1 STILL. 820. G G O O 819 .5 8 1 9 . 5 0 0 782 . 0 150 8 6 4 . 5 150 0 . 0 0. 0 0 0 0 . 0 0. 0 0 G 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 O.G 0 . 0 0 0 4 7 7 0 . 1 4 7 7 0 . 8 2 2 . 0 1 NOB SL= 2 NOB SR= 2 SOI L 822. 0 O O P 821. 5 8 2 1 . 5 P P 7 7 6 . 5 150 8 5 9 . 0 150 0 . 0 0. 0 0 G 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 . 0 0 0 4 8 7 0 . 1 NOB 5 L : 4 8 7 0 . NOBSR-" 821. 0 .1 2 SC IL 821. 0 O O P 820.5 8 2 0 . 5 0 G 7 6 0 . 5 150 835, 5 150 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0. 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 o.o 0 0 0. 0 0 . 0 0 0 4970 . 1 4 9 7 0 . 8 1 3 . 0 1 8 1 3 . 0 NCBSL= 2 NOBSR= 2 SC IL = 0 0 0 8 1 2 . 5 812. 5 0 0 7 7 5 . 0 150 827 .5 150 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0. G 0 . 0 0 0 0. 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0. G 0 0 5 0 7 0 . 1 5 0 7 0 . 8 3 1 . 0 1 8 3 1 . 0 NGBSL= 2 NOBSR= 2 SOIL = 0 0 0 83 0.5 83 0 .5 0 0 7 4 0 . 5 150 8 8 3 . 0 150 0. G 0 .0 0 0 0. G 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0 . 0 0. 0 0 0 0 . 0 0. G 0 0 5 1 7 0 , 1 5 1 7 0 . 8 4 2 . 2 1 842 .2 N0BSL= 2 NOBSR= 2 SOIL = O O P 8 4 1 . 7 8 4 1 . 7 P 0 8 1 9 , 2 150 9 1 6 . 7 150 0. 0 0 . 0 0 0 0. 0 0 . 0 0 G 0 . 0 0. 0 0 0 0 .0 0. 0 0 0 0 .0 o.o 0 0 0 . 0 0 . 0 0 0 5 2 7 0 . 1 5270 . 8 5 7 . 0 1 857. 0 NOBSL= 2 NOB SR= 2 SOIL = G O O 8 5 6 . 5 8 5 6 . 5 C 0 871 .5 150 8 5 6 . 5 150 0. 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0 .0 0 0 0. 0 0 . 0 0 0 CHAIN EQ COR CHG GND ELV Q COR ELV 8 SETS OF ELEV + DISTANCES - L E F T SIDE - TOP ROW,RIGHT SIDE - BOTTOM ROW 1ELEV 1DIST 2ELEV 2D I ST 3ELEV 3D I ST 4ELEV 401 ST 5ELEV 5 CI ST 6ELEV 6DIST 7 EL EV 7 0 IS T 8ELEV 8DI 5 4 2 0. 1 5420 . 860. 1 1 660. 1 NOB SL= 2 NOBSR= 2 SOIL = O O P 8 5 9 . 6 8 5 9 . 6 0 0 829 .6 150 867.1 150 0 .0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0. C 0 . 0 c 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 5 4 7 0 . 1 5470 . 87 1. 0 1. 871. G NCBSI = 2 NOBSR= 2 SOIL - O O P 870.5 870. 5 P 0 8 4 0 . 5 150 885.5 150 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0. 0 0 0 5570 . 1 5 5 7 0 . 8 7 5 . 0 1 8 7 5 . 0 8 7 4 . 5 0 8 2 2 . 0 150 0 . 0 0 0 . 0 C O.G 0 0 .0 0 0 .0 0 0 . 0 0 874 .5 0 9 1 9 . 5 150 p.O 0 0 . 0 0 0 . 0 0 0 . 0 0 ' 0 . 0 0 0 . 0 0 NCBSL= 2 N08SR= 2 SOIL = O O P , , , . 5 6 7 0 . 1 5 6 7 0 . 912 .0 1 9 1 2 . 0 91 1. 5 0 881 . 5 150 0. 0 0 0. 0 0 0. 0 0 0 . 0 0 0 . 0 0 911 .5 0 9 8 6 . 5 150 0 . 0 0 0 . 0 0 0 , 0 0 0 . 0 0 0 . 0 0 NOBSL- 2 NOBSR= 2 SOIL = G O O . . . _ 0 . 0 0. 0 0 0 5 7 7 0 . 1 5 7 7 0 . 9 1 9 . 0 1 9 1 9 .C 918 . 5 0 851 . 0 150 O.G 0 0 . 0 0 0 . 0 0 9 1 8 . 5 0 9 7 1 . 0 150 0 . 0 0 0 .0 0 0 .0 0 NOBSL- 2 NOSSR= 2 SO I L - O O P . _ _ _ 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 5 8 7 0 , 1 5 8 7 0 . 9 2 8 . 0 1 928 .0 9 2 7 . 5 G 837 .5 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 9 2 7 . 5 G 1 0 0 2 . 5 150 P.O 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 J_Ji_B_SJL=_2 NOBSR= 2 SOIL = G O O , , _ 5 9 7 0 . 3. 5 9 7 0 . 936. 0 1 936. C NCBSL= 2 NOB SR= 2 SOIL = O O P 935 .5 0 8 6 8 . 0 150 0 . 0 0 0 . 0 0 0 . 0 9 3 5 . 5 0 1 0 1 0 , 5 150 O.G 0 0 . 0 0 0 . 0 0 0 0 . 0 0 .0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 6G70. 1 6 0 7 0 . 9 3 4 . 0 1 934. 0 CHAIN EQ COR CHG GNO ELV 0 COP ELV 8 SETS OF ELEV + D ISTANCES - L E F T SIDE - TOP ROW,RIGHT S IDE - BOTTOM ROW 1ELEV 1DIST 2ELEV 2DIST 3 ELE V 3D.IST 4ELEV 401ST 5ELEV 501 ST 6 EL EV 60 IST 7ELEV 7DIST 8ELEV 8DI 617C. 1 6170 . 9 4 6 . 0 1 NOBSL= 2 NOBSR= 2 SC IL 946. G O O P 9 4 5 . 5 P 8 7 8 . P 150 . 0 . 0 0 0 . 0 0 0. C 0 0. 0 0 0 . 0 0 0 . 0 0 945. 5 0 1020 . 5 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 6 2 7 0 . 1 NOBS L : 62 7 0 . 9 5 2 . 5 1 NOBSR= 2 SOIL 952 .5 0 0 0 9 5 2 . 0 0 8 8 4 , 5 150 0. 0 0 0. 0 0 0. 0 0 0. 0 0 0 . 0 0 0 . 0 0 9 5 2 . 0 0 1 0 0 4 . 5 150 0 . 0 0 0 , 0 0 0 . 0 0 0 . 0 0 0. 0 0 0. 0 0 6 3 7 0 . 1 6 3 7 0 , 9 7 1 . 0 1 9 7 1 . 0 NQBSL= 2 NOBSR= 2 SOIL = O O P 9 7 0 . 5 0 903 . 0 150 0. 0 G 0. 0 0 0 , 0 0 0 . 0 0 0 . 0 0 0 . 0 0 9 7 0 . 5 0 1 0 4 5 . 5 150 0 . 0 0 0 . 0 0 0. 0 0 O.G 0 0 . 0 0 0 . 0 0 6 4 2 0 . 1 6 4 2 0 . NOBSL= 2 N0BSR= 9 8 0 . 5 1 9 8 0 . 5 2 SOIL = 0 0 0 9 8 0 . 0 0 905 . 0 150 0. 0 0 0. 0 0 0 . 0 0 0 . 0 0 0 .0 0 9 8 0 . 0 0 1 0 5 5 . 0 150 0 . 0 0 0 . 0 0 0. 0 0 0. 0 0 0 . 0 0 0 . 0 0 . 0 0 0 6 4 7 0 . 1 64 7 0 . 99 1.0 1 991 . 0 NOBSL= 2 NOBSR= 2 SOIL = G O O 990. 5 0 893. 0 150 0 . 0 0 0 , 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 990 .5 0 1 0 7 3 . 0 150 0. 0 0 O.G 0 0. 0 0 0 . 0 0 0 . 0 0 0 . 0 0 6 5 2 0 . 1 6520 . 9 8 6 . 2 1 NOBSL= 2 NQB$R= 2 S O U <86. 2 0 0 0 985. 7 0 8 8 0 . 7 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 9 8 5 . 7 0 1053. 2 150 0. 0 0 0. 0 0 0 . 0 0 0 . 0 0 0 . 0 0 G. 0 0 . 0 0 0 6 5 7 0 . 1 6570 . NOBSL= 2 NOBSR' 9 8 5. 0 1 9 6 5 . 0 2 SC IL = O O P 984 .5 0 8 9 4 . 5 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 9 8 4 . 5 0 1 0 6 7 . C 15 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 CHAIN EC COR CHG GNC ELV Q COR ELV 8 SETS OF ELEV + 01 STANCES - LEFT SIDE - TCP ROW , RIGHT S I C E - BOTTOM ROW 1ELEV 1DIST 2ELEV 2D 1ST 3ELEV 3 DIST 4 ELEV 4DIST 5ELEV 5DIST 6ELEV 6DI ST 7 ELEV 7DIST 8ELE V 8DI J 6 6 7 0 . NORSi = 1 2 6670 . NOBSR= 9 8 7 . 0 _____SOJi_ 1 987 .0 0 0 0 9 8 6 . 5 986. 5 0 0 9 2 6 . 5 1 0 3 9 . 0 150 150 0. 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0. 0 0 S 0 6 7 2 0 . N.O.B_S.L = 1 _2_ 67 2 0 . NOB_SR = 985 .1 ______ LL_ 1 98 5. 1 0 0 0 9 8 4 . 6 984 .6 0 0 9 5 4 . 6 1044 .6 150 150 0. G 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 .0 0. 0 0 0 0 . 0 0. 0 0 0 6770 . NOBSL= 1 2 6 7 7 0 . NOBSR = 9 8 5 . 0 2 SOIL 1 9 8 5 . 0 0 0 0 984. 5 9 8 4 . 5 0 0 939 . 5 1 0 5 2 . 0 150 150 0. 0 0 . 0 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0. C 0 0 0 . 0 0 . 0 0 0 O.G 0 . 0 0 0 6 8 2 0 . bLQBJSL = 1 2 68 20 . NOB SR = 9 8 8 . 0 2... SC.I L 1 S88. 0 0 0 0 987. 5 9 8 7 . 5 0 0 920 . 0 1 0 5 5 . 0 150 150 0 . 0 0. 0 0 0 0 . 0 0. G 0 0 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 .0 0 0 0. c 0 . 0 0 0 6 8 7 0 . NOBSL= 1 2 6 8 7 0 . NGBSR-991 . 0 2 SGIL 1 991. C 0 0 0 990 . 5 990 . 5 0 0 9 5 3 . 0 1050. 5 150 150 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 .0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 697C. NOB SI = 1 2 6 9 7 0 . NOBSR= 1G02.0 _ 2 S C J L . 1 1 0 0 2 . 0 0 0 0 1 0 0 1 . 5 1001. 5 0 0 9 4 9 . 0 1054. 0 150 150 0 .0 0. 0 0 0 0 . 0 0 , 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0 . 0 0. 0 0 0 7 0 7 0 . NGBSL= 1 2 7 0 7 0 . NOBSR= 1 0 0 6 , 0 2 SOIL 1 1 006 .0 0 0 0 1005 .5 1 0 0 5 . 5 0 0 1 0 0 5 . 5 1 0 5 8 . 0 150 150 0. 0 0 . 0 0 0 O.G 0 . 0 0 0 0. 0 0 . 0 0 0 0 .0 0 . 0 0 0 0 . 0 o . 0 0 0 0 . 0 0. 0 0 0 7 0 9 5 . NCBSL= 1 2 7095 . NOBSR= 1010 ,0 2 _ s o a 1 1010.0 0 0 0 1 0 0 9 . 5 1 0 0 9 . 5 0 0 1 0 3 9 . 5 1 0 6 9 . 5 15G 150 O.G 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 .0 0. 0 0 0 0 . 0 0. 0 0 0 CHAIN EG COR CHG C-N D ELV Q COR ELV 8 SETS OF ELEV + DISTANCES - LEFT S ICE - TCP ROW, RIGHT S IDE - BOTTOM ROW 1.ELEV 1DIST 2 EL EV 2D 1ST 3 EL EV 3DIST 4ELEV 40IST 5ELEV 5DIST 6ELEV 601 ST 7ELEV 7 DIS T 8E LEV 8DI 7 1 4 5 . 1 7 1 4 5 . 1014 .4 1 1014.4 NOBSL= 2 NOBSR= 2 SOIL C O O 1013.9 G 1051. 4 150 0 . 0 C 0. 0 0 0 . 0 0 0 . 0 0 1013 .9 0 1036 .4 150 0 .0 0 0 . 0 0 0. 0 0 0. 0 0 0 .0 0. 0 0 0 0 . 0 0. 0 0 0 7 1 9 5 . 1 7 1 9 5 . 1023.1 1 1023.1 NOBSL= 2 NOBSR= 2 SOIL = O O P 1G22.6 0 1060.1 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 1 0 2 2 . 6 0 1015.1 150 0 . 0 0 0 .0 G 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 7 2 4 5 . 1 7 2 4 5 . 1024.3 1 1024.3 1023.8 1023.8 NOBSL= 2 NOBSR= 2 SCIL = 0 0 0 G 1076 .3 150 0 . 0 0 0 . 0 0 0 9 6 3 . 8 150 0. 0 0 0. 0 0 0 . 0 0. C 0 0 O.G 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 . 0 0 0 7274 . 1 7 2 7 4 . 1025. 0 1 1025. 0 1C24 .5 1024 .5 NOB S L - 2 NOBSR= 2 SOIL = O O P  0 1 P 9 9 . 5 150 0 . 0 0 0 . 0 G 0 . 0 0 0 957 . 0 150 0. 0 0 0. 0 0 0 . 0 0 0 , 0 0 . 0 0 0 0. 0 o.o 0 0 0. 0 0 .0 0 0 7 2 9 5 . 1 7295 . 1 0 2 3 . 0 1 1G23.0 1 0 2 2 . 5 0 102 2. 5 C NOBSL= 2 NOBSR= 2 SC IL = O O P  I I P 5 . 0 150 9 8 5 . 0 150 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0. 0 0 0 7 4 5 0 . 1 7 4 5 0 . 1014.0 1 1014 .0 1 0 1 3 . 5 1 0 1 3 . 5 NGBSL= 2 N08SR. = 2 SOIL ~ C O O 0 1 0 2 8 . 5 150 0 . 0 0 0. 0 G 0 .0 0 1 0 0 6 . 0 150 0 , 0 0 0 . 0 0 0 .0 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 7 5 5 0 , 1 7 5 5 0 . 1 0 0 7 . 0 1 1007 .0 1 0 0 6 . 5 1 0 0 6 . 5 NOBSL= 2 NOBSR= 2 SOIL = O O P  0 1P06. 5 150 O.G 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 1 0 0 6 . 5 150 0 .0 0 0 . 0 0 0 . 0 0 O.G 0 0 . 0 0 0 . 0 0 CHAIN EQ COR CHG GND ELV C COR ELV S SETS OF ELEV + DISTANCES - LEFT SIDE - TOP ROW,RIGHT SIDE - BOTTOM ROW 1 EL EV 1DIST 2ELEV 2DIST 3ELEV 3DIST 4ELEV 4DI ST 5ELEV 50IST 6ELEV 6DIST 7 ELEV 7DIST 8ELEV 8DI 7 7 5 0 . 1 7 7 5 0 . NOBSL= 2 NOBSR= 1030 .0 1 1030. 0 1029. 5 C „ * 1 0 2 9 . 5 0 2 SOIL = 0 0 0  1022. 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 1 0 2 2 . 0 150 0. 0 0 0. 0 0 0. 0 0 0 . 0 0 0 . 0 0 0 0. 0 0 . 0 0 0 7 8 5 0 . 1 7 8 5 0 . 1020. 0 1 1C20. 0 1019 .5 1 0 1 9 . 5 NC»BSL = 2 NOBSR= 2 SOIL = O O P  0 9 9 7 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 . 0 . 0 0 0 . 0 0 0 1064. 5 150 0. 0 0. 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 7 9 5 0 . 1 7950 . 1055 .0 1 1 0 5 5 . 0 ' 1 0 5 4 . 5 10 54 .5 NOB SL= 2 NG8SR= 2 SOIL = O O P  0 1092 .0 150 0 . 0 0 0 . 0 0 0 . 0 0 C O 0 0. 0 0 0. 0 0 G 1 0 5 4 . 5 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 8000. 1 8 0 0 0 . 1 0 6 5 . 0 1 1065.0 1 0 6 4 . 5 1 0 6 4 . 5 NOBS L= 2 NOBSR= 2 SOIL = O O P 0 1 1 0 9 . 5 150 0. 0 0 0 . 0 0 0. 0 0 0 . 0 0 0 . 0 0 0 .0 0 0 1 0 2 7 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 0 . 0 0 8 0 5 0 . 1. 8 0 5 0 . 1 0 7 5 . 0 1 1075 .0 1 0 7 4 . 5 1 0 7 4 , 5 NOBSL= 2 NOBSR= 2 SOIL = G O O G 1 0 9 7 . 0 150 O.G 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 1 0 5 9 . 5 150 0 . 0 0 0 . 0 0 O.G 0 0 . 0 0 0 . 0 0 0 .0 0 8 1 0 0 . 1 8 1 0 0 . 1073.6 1 1C73.6 1073 .1 107 3.1 jmB_Sj___2 Ni).B..S.R= 2...SQIL___ .0 .0 ....0 G 1020. 6 150 0. 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 .0 0 0 1043.1 150 0 . 0 0 0 . 0 0 O.G 0 0, 0 0 0 . 0 0 0 . 0 0 8 1 5 0 . 1 8150 . 1 0 7 0 . 0 1 1C70 .0 1G69.5 C 1069 .5 0 NOBSL= 2 NOBSR= 2 SOIL •= G O O  9 8 7 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 , 0 0 O.G 0 1 1 5 2 . 0 150 0, 0 G 0. 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 1 0 2 0 . 0 150 0 . 0 0 0 .0 0 0 . 0 0 0 . 0 0 0. 0 0 0. 0 0 0 1 1 3 2 . 5 15G 0. 0 0 0 .0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 CHAIN EG COP CHG GNC ELV G COR ELV 8 SETS OF ELEV + DISTANCES - L E F T SIDE - TCP RCW,RIGHT S ICE - BOTTOM ROW 1ELEV 1DIST 2ELEV 2D I ST 3ELEV 30 IST 4ELEV 4DIST 5ELEV 5DIST 6 ELEV 6CIST 7ELEV 7DIST 8ELEV 8DI 8 2 5 0 . 1 8250. 1C76.0 1 1C76.C NOB S L= 2 NOBS R = 2 SOIL 1075 .5 0 1 0 5 3 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 O.G 0 1075. 5 0 1098. 0 150 0. 0 0 0 . 0 0 0 . 0 0 0 .0 0 O O P 0. 0 0 . 0 0 0 C. G 0 .0 < 8300. 1 8300 . 1 C82 .0 1 1G82.0 1 0 8 1 . 5 1081. 5 NOBSL- 2 NOB SR= 2 SC IL = O O P  0 10 5 1 . 5 150 0 .0 0 0 . 0 0 0. 0 0 0. 0 0 0 .0 0 0 . 0 0 0 1104. 0 1 5 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 .0 0 O.G 0 8350 . 1 8 3 5 0 . 1 0 8 2 . 0 1 1 0 8 2 . 0 1 0 8 1 . 5 1 0 8 1 . 5 N0BSL= 2 NGBSR= 2 SOIL = O O P 0 1 0 2 9 . 0 150 0 .0 0 0. 0 C 0. C 0 0 . 0 0 0 . 0 0 0 . 0 0 0 1 1 7 9 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 0. 0 0 8 4 5 0 . 1 8 4 5 0 . 1092 .0 1 1092 .0 1091. 5 0 1016. 5 150 0. 0 0 0. 0 0 0 . 0 0 0 .0 0 0 . 0 0 0 . 0 0 1 0 9 1 . 5 0 1 1 5 9 . 0 150 p . p p 0 . 0 0 0 . 0 0 0 . 0 0 0 .0 0 0 . 0 0 NCBSL= 2 NOBSR= 2 SOIL = 0 0 0 . 8 5 5 0 . 1 8 5 5 0 . 1 1 0 8 . 0 1 1108.0 1 1 0 7 . 5 0 1 1 0 7 . 5 0 NOBSL- 2 NOBSR- 2 SOIL = O O P  1 0 3 2 . 5 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 1 1 3 0 , 0 150 0. 0 0 0. 0 0 0. 0 0 0 . 0 0 0 .0 0 0 0. 0 0 . 0 0 0 8 6 0 0 . 1 8 6 0 0 . 1101 .0 1 1101 .0 1 1 0 0 . 5 1 1 0 0 . 5 NOBSL= 2 NOBSR= 2 SOIL = O O P  0 1093 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 1130. 5 150 0. 0 0 0. 0 0 0 .0 0 0 . 0 0 0 . 0 0 0 0. c 0 . 0 0 0 € 6 5 0 . 1 8650. 1096. 0 1 1C96. 0 1 0 9 5 . 5 1 0 9 5 . 5 NOBSL= 2 NOBSR= 2 SC IL = O O P  0 1 1 0 3 . 0 150 P.O 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 1155. 5 150 0. 0 0 0 . 0 0 0 . 0 0 " 0 . 0 0 0 . 0 0 0. 0 0 . 0 0 0 CHAIN EC COR CHG GND ELV Q COR ELV 8 SETS OF ELEV + DISTANCES - LEFT SIDE - TCP ROW,RIGHT SICE - BOTTOM ROW 1ELEV 1DIST 2 ELEV 2D 1ST 3ELEV 3DIST 4ELEV 4DIST 5ELEV 501 ST 6ELEV 6DI ST 7ELEV 701 ST 8E LE V 8DI 875 0. NCBSI = 1 2 8750. NOBSR= 109 8.0 2 SOIL 1 1098.0 0 0 0 1097.5 1097. 5 0 0 1082.5 1135.0 150 150 0. 0 0.0 0 0 0.0 0.0 c 0 0. 0 0.0 0 0 0.0 0.0 G 0 0.0 o. 0 0 0 0.0 0. 0 0 N 0 8800. _ NX8.SL = „ 1 2 8800 . NOBSR= 1 100 .0 _2_PLL 1 1100.0 G O O 1099.5 1099.5 C 0 1024.5 1129 .5 150 150 0. C 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 0.0 0.0 0 0 0 .0 0. 0 0 0 0.0 0. 0 0 0 -8850 . NOBSL= 1 2 8850 . NOBSR= 1102.0 2 SOIL 1 1102.0 G O O 1101. 5 1101 .5 0 0 1019. 0 1161.5 150 150 0. 0 O.G 0 0 0.0 0.0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 O.G 0.0 0 0 8900. NOBSL= 1 2 8900. NOB SR = 1107.0 2 SOIL 1 11C 7.0 0 0 0 1106. 5 1106.5 0 0 1039.0 1129.0 150 150 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 o.o 0 0 0. 0 0.0 0 0 8950. NGB SL = 1 2 8950. NGB SR = 1111.0 2 SOIL 1 1111.0 0 0 0 1 110. 5 1110.5 0 0 105 8.0 1170. 5 150 15G 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0.0 0 0 0.0 0 .0 C 0 0. 0 0.0 0 0 0. G 0.0 0 0 9050. N.QB SJL__ 1 2 9050. NGBSR= 1115.0 2 SCIL 1 1115.0 0 0 0 1114.5 1114. 5 0 0 1084.5 1197. 0 150 150 0 .0 0. 0 0 0 0.0 0.0 c 0 0. G 0.0 0 0 0. 0 0.0 0 0 0.0 0.0 0 0 0. 0 0. 0 0 0 9100. NCBSL= 1 2 91 00. N G B S R = 1110.2 2 SOIL 1 1110.2 0 0 0 1109.7 1109. 7 0' 0 1079.7 1169.7 150 150 0. c 0.0 C 0 0.0 0.0 c 0 0. 0 0.0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 0.0 0. 0 0 0 9150. NOBSL= 1 2 9150 . N0BSR= 1104 .0 2 SOIL 1 1104.0 0 0 0 1103.5 1103.5 0 0 1058.5 1141.0 150 150 0. 0 0.0 0 0 0. 0 0.0 0 0 0. 0 0.0 0 0 0.0 0.0 0 0 0 .0 0. 0 0 0 0.0 G. 0 0 0 CHAIN EQ COR CHG GND ELV 0 COR ELV 8 SETS OF ELEV + DISTANCES - LEFT S IDE - TOP ROW, RIGHT S IDE - BOTTOM ROW 1ELEV 1DIST 2ELEV 2DIST 3 ELEV 3D I ST 4ELEV 4DIST 5ELEV 5DIST 6ELEV 60 IST 7E LE V 7DI ST 8ELEV 8DI 9 2 0 0 , 1 9 2 0 0 . 1105 .6 1 1105.6 NOBSL= 2 NOBSR-: 2 SOIL O O P 1 105. 1 0 1052. 6 15G O.G 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 1105 . 1 0 1 1 2 7 . 6 150 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 0 . 0 0 0 . 0 0. 0 0 0 9 2 5 0 . 1 9 2 5 0 . 1 1 0 7 . 0 1 1107.0 NOBSL= 2 NOBSR- 2 SOIL = O O P 1106 .5 C 1 0 5 4 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 1 1 0 6 . 5 0 1 1 4 4 . 0 150 0 . 0 0 0.0 0 0 . 0 0 0 .0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 9 3 5 0 . 1 9 3 5 0 . 1111.8 1 1111 ,8 1 1 1 1 . 3 0 1 0 5 8 . 8 150 0 . 0 0 0 . 0 0 1111 .3 0 1148 .8 150 0 . 0 0 0 . 0 0 NOB SL - 2 NOBSR= 2 SOIL = O O P . 0 . 0 0. 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 0 . 0 0 94GG. 1 9400 , 1107.1 1 1107.1 1 1 0 6 . 6 0 1046 .6 150 0 . 0 0 0 . 0 0 1 1 0 6 . 6 0 1 1 6 6 . 6 150 0 .0 0 0 . 0 0 NOBSL- 2 NOBSR- 2 SC IL = O O P  O.G 0 . 0 0 0 0 . 0 0 . 0 0 0 0. 0 0 . 0 0 0 0. 0 0 . 0 0 0 9450 . 1 9450 . 1 1 0 3 . 0 1 1 1 0 3 . 0 1102 .5 0 1 0 4 2 . 5 150 0 . 0 0 0 . 0 0 0 . 0 0 1 1 0 2 . 5 0 1 1 5 5 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 NC8SL= 2 N C 8 S R - 2 SC IL = O O P . . . , 0. 0 0 . 0 0 0 0 . 0 0 . 0 0 0 0 . 0 0. 0 0 0 9 5 0 0 . 1 9 5 0 0 . 1 1 0 0 . 0 1 1100.0 1099 .5 0 1 0 4 7 . 0 150 0. 0 0 0. 0 0 0 . 0 0 1 0 9 9 . 5 0 1 1 3 7 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 NG3.SL=_ .2 _NCB.S.R= 2_S_aiL___ G_J0_Q ._„ . 0 . 0 0 . G 0 0 0 . 0 0. 0 0 0 0 . 0 0. 0 0 0 9 5 5 0 . 1 9 5 5 0 . 1097 .0 1 1097 .0 1096. 5 0 1059 . 0 150 0. 0 0 0. 0 0 0 . 0 0 0 . 0 0 0 . 0 0 1 0 9 6 . 5 0 1 1 2 6 . 5 15 0 0 . 0 0 0 . 0 0 0. 0 0 0. 0 0 0 . 0 0 NOBSL= 2 NOB SR - 2 SOIL = O O P , , , . 0.0 0.0 0 0 CHAIN EQ COR CHG GND ELV C COR ELV 8 SETS OF ELEV + DISTANCES - L E F T S IDE - TOP ROW,RIGHT SIDE - BOTTOM ROW 1 EL EV 1DIST 2ELEV 2D I ST 3ELEV 3DIST 4ELEV 401 ST 5ELEV 5DIST 6ELEV 601 ST 7 ELEV 7DIST 8ELEV 8DI 9 6 1 2 . 1 9 6 1 2 . 1C95.C 1 109 5.C NOBSL= 2 NOBSR= 2 SOIL = C O O 1094. 5 0 1087. 0 150 0 . 0 0 0 . 0 0 . 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 1094. 5 0 1 1 0 2 . 0 150 0. 0 0 0. 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 9 6 4 1 . 1 9 6 4 1 . 1094. 0 1 1 0 9 4 . 0 NOB.SL= 2 MOB SR. = 2 SOIL = O O P 1093. 5 0 1 0 8 6 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 O.G 0 1 0 9 3 . 5 0 1 1 0 1 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 .0 0 0 . 0 0 9 7 0 0 . 1 9 7 0 0 . 1103 .7 1 1103 .7 1 1 0 3 . 2 1103. 2 NOBSL= 2 N0BSR= 2 SOIL = O O P  P 1 0 9 5 . 7 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 .0 0 0 1103.2 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 9 7 5 0 . 1 9 7 5 0 . 1 1 1 4 . 0 1 1 1 1 4 . 0 1 1 1 3 . 5 0 1 1 0 6 . 0 150 0 . 0 0 0 . 0 C 0 . 0 0 0 . 0 0 0 . 0 0 1 1 1 3 . 5 0 1 1 2 8 . 5 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 ' 0 0 . 0 0 NOBSL= 2 NOBSR= 2. SO IL = O O P . : 0 . 0 0. 0 0 0 9 8 5 0 . 1 9 8 5 0 . 1119 .0 1 1 119.0 1 1 1 8 . 5 0 1 0 9 6 . 0 150 0 . 0 0 O.G G O.G 0 0 . 0 0 0 . 0 0 0 . 0 0 1 1 1 8 . 5 0 1 0 9 6 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 NOBSL= 2 NOB.SR= 2 SOIL = 0 G 0 ___________^^ . . . 9 9 5 0 . 1 9 9 5 0 . 1 1 2 8 . 0 1 1128.0 1 1 2 7 . 5 0 1 1 0 5 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 1 1 2 7 . 5 0 1 1 2 0 . 0 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 NOBSL= 2 NOBSR= 2 SOIL = O O P „ 0 0 O.G 0 . 0 0 0 1 0 0 5 0 . 1 1 0 0 5 0 . 1 1 2 8 . 0 1 1128.0 1127. 5 0 1097 . 5 150 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0. 0 0 1 1 2 7 . 5 0 1 1 3 5 . 0 150 0. 0 0 0. 0 G 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 N0BSL= 2 NOBSR= 2 SOIL = G O O . . _ A P P g M p i V 2. VOLUMi? CAt.CAil AT [OK) THESIS PROJECT, UNIVERSITY OF BRITISH COLUMBIA RESEARCH FOREST; ROAD C CHAINAGE ELEVATN SLOPES SHRINK SWELL 0. M. ROCK DITCH S CRAP ER SUBGRADE EXCAVATION F I L L SI DECAST NE T BACK CUT F ILL DI TCH DITCH SLOPE Dl TCH WIDTHS ACC F ILL RK CM DEPTH DEPTH W IDTH LEFT RIGHT ROCK OM MASS 1+00 5 0 7 . 0 5.00 1.3 3 1. 00 1. 33 1. CO 1.00 1 . 00 0 . 5 0 0 13 13 0 0 0 0 0 0 , 2+00 514 ,0 5.00 1.33 I.00 1. 33 1.00 1 .00 1.00 0 , 5 0 0 13 13 0 175 19 19 156 0 ) 3+00 5 2 1 . 0 5. GO 1.3 3 1. GO 1. 33 1.00 1 .00 1 .00 0 .50 0 13 13 0 180 10 10 327 0 3+.5.0 . ._,5.24_.5„__ _i..OjO._L.__ _ _1.._0_0_ 1..33 1 . 00 1.00 1. 00 0. 50 0 13 13 0 61 5 5 3.82 _ 0 4+00 5 2 8 . 0 5.00 1.33 1 .00 1.33 1.00 1 .00 1.00 0 . 5 0 0 ' 15 15 0 135 0 0 517 0 5+00 5 3 5 . 0 5.00 1.33 1. CO 1.33 , 1. 00 1 .00 1.00 0 . 5 0 0 15 15 0 180 657 1 80 40 0 5 + 50 5 3 8 . 5 5.00 1 .33 1.00 1.3 3 1. 00 1.00 1. GO 0. 50 0 1 5 15 0 0 616 0 - 5 7 6 0 6+00 5 4 2 . 0 5.00 1.33 1 .00 1 .33 1 .00 1.00 1.00 0 .5 0 0 15 15 0 0 418 0 - 9 9 4 0 7 + 00 5 4 9 . 0 5.00 1.3 3 1.00 1. 33 1. CO 1.00 1.00 0 . 5 0 0 13 13 0 404 261 261 - 8 5 1 0 ..8 + 00.... .__553_.A__ . 5_. .0.0 1...3 3 X._00 X. 33 .1.00 1.00 1 . 0 0 C . 50 0 13 13 0 843 ' 0 0 -8 0 8+ 50 5 5 7 . 8 5 .00 1.33 1.00 1.33 1.00 1 .00 1 .00 0 .50 0 13 13 0 312 2 2 302 0 9 +00 5 5 8 . 4 5.00 5.00 1.00 1. 33 1. GO 1 . CO 1. 00 0.5 0 0 13 13 0 135 45 45 392 0 10 + 00 5 5 7 . 0 5 .00 5.00 1 .00 1 .33 1.00 1.00 1.00 0 .5 0 0 14 14 0 175 218 175 348 0 11+00 5 5 5 . 4 5.00 1 .33 1. 00 1.33 1 . 00 1 .00 1.00 0 . 5 0 0 14 14 0 115 506 115 - 4 3 0 12+00 5 5 3 . 8 5.00 1 .33 1.00 1. 33 1.00 1. 00 1. 00 0. 5 0 0 14 14 0 24 1100 24 - 11 19 0 13+00.. . - 5,5-2... 1 5_.JD_0. .L..33 _1 . o.o L..33 1.00 1 .00 1.00 0 . 5 0 0 14 14 0 0 . 2XL3 0 -3231 . 0 13 + 20 551 . 8 5.00 1.33 1. 00 1.33 1. 00 1.00 1 . 00 0 . 5 0 0 14 14 0 0 5 83 0 - 3 8 1 4 0 13 + 67 551 .1 5 .00 1.33 1.00 1.3 3 1. 00 1. 00 1. OG 0 .5 0 0 15 15 0 0 1440 0 - 5 2 5 4 0 14+00 5 5 0 . 5 5 .00 1.33 1. 00 1.33 1 .00 1 .00 1 .00 0 ,50 0 15 15 0 0 1171 0 -642 5 0 15+00 548 .9 5.00 1.33 1. 00 1. 33 1. CO 1.00 1 . 00 0 , 5 0 0 15 15 0 1738 2012 17 38 - 6 6 9 9 G 15+73 547 .7 5.00 1.33 1.00 1*. 33 1.00 1.00 1.00 0 . 5 0 0 1 5 15 0 2909 0 0 - 3 7 9 0 0 16 + C.C_„. 5.4J...2 5.. 0_0 l.._33 _L_LQ_ 1..33 1 .00 1_. 00 1 .00 0 .50 0 15 15 G 1204 0 0 .. - 2586 . ... .0 16+34 5 4 6 . 7 5.00 1.33 1.00 1. 33 1.00 1.00 1. 00 0. 50 0 17 17 0 1654 0 0 - 9 3 2 0 17+00 5 4 6 . 1 5 .00 1.33 1 .00 1.33 1.00 1.00 1.00 0 . 5 0 0 17 17 C 205 1 0 0 1119 0 18+00 5 4 8 . 7 5.00 1.33 1. GO 1. 33 1. 00 1 . 00 1.00 0 , 5 0 0 17 17 0 454 3146 454 - 1 5 7 3 0 18 + 31 550 .4 5.00 1.33 1.00 1.33 1. 00 1. 00 1. 00 0. 50 0 17 17 0 0 2263 0 - 3 8 3 6 0 18+90 554. 7 5 .00 1.33 1 .00 r. 33 1.00 1 .00 1 .00 0 . 5 0 0 17 17 0 0 3580 0 - 7416 0 19 + 00 .. 555 .6 5.00 1.3 3 L._0X) 1.. 33 L. 0.0 L» 0.0 1_. OA. 0 . 5 0 0 17 17 0 0 368 0 - 7784 0 20 + 00 565 .0 5.00 1.33 1.00 1. 33 1.00 1.00 1.0 0 0 . 5 0 0 17 17 0 0 2340 0 - 1 0 1 2 4 0 21 + 00 5 7 4 . 5 5.00 1.33 1. 00 1. 33 1 .00 1 .00 1 .00 0 . 5 0 0 17 17 0 140 573 140 - 1 0 5 5 8 ' . 0 22+00 583 .9 5.00 1.33 1.00 1. 33 1. GO 1. 00 1,00 0 .5 0 0 17 17 0 59 9 0 0 - 9 9 5 9 0 23+70 5 9 9 . 9 5.00 1.33 1 .00 1'.33 1.00 1 . 00 1.00 0. 50 0 17 17 0 2163 0 0 -7796 0 24 + 70 6 0 9 . 3 5. 00 5. 00 1. 00 1. 33 1. 00 1 .00 1.00 0 .50 0 17 17 0 2388 0 0 - 5 4 08 o-_ 25+15 _._6.1.3.._6__ _5...0.O_.5_._0JG_ L. 0.0 1.33 . . _ L . OH 1 . 00 L. OIL 0... 5 0 0 1 7 I J . o_ . .1.14.9 . 0 0 -4258. 0 2 5+70 618 . 8 5.00 5 .00 1 .00 1.33 1.00 1 .00 1.00 0 .5 0 0 17 17 G 1051 0 0 - 3 2 0 7 0 26+70 6 2 8 . 2 5.00 5.00 1.00 1. 33 1. 00 1. 00 1.00 0.5 0 0 17 17 0 2037 0 0 - 11.71 0 27 + 70 6 3 7 . 5 5 .00 5 .00 1.00 1.33 1. 00 1. 00 1. GO 0. 50 0 17 17 G 2 630 0 0 1460 0 28+70 6 4 4 . 8 5.00 1.33 1. 00 1. 33 1.00 1 .00 1 .00 0 .50 0 17 17 0 2956 0 0 4416 0 28+77 6 4 5 . 2 5.00 1.33 1 .00 1'. 33 1. 00 1. 00 1 . CO 0 .5 0 0 17 17 0 190 0 0 4606 0 .. . 2 9 + 52... _.._6__9_._1 _5_._0i3_.L.33_ 1_.D.0 1.33 l . CO 1 .00 1 . 00 0 , 5 0 0 17 17 0 1 004 17 17 5593 ._ 0 29 + 70 6 5 0 . 0 5.00 1.33 1. CO 1. 33 1 .00 1 .00 1 .00 0 . 5 0 0 17 17 0 15 16 15 55 92 0 30+70 6 5 4 . 9 5.00 1.33 1.00 1. 33 1. 00 1. 00 1. CO 0. 50 0 1 7 17 0 225 83 83 5735 0 31+24 6 5 7 . 7 5 .00 1.33 1 .00 1 .33 1 .00 1.00 1.00 0 ,50 0 13 13 G 119 43 43 5812 0 31 + 70 6 6 0 . 4 5.00 1.33 1. 00 1. 33 I. 00 1.00 1 . 00 0.5 0 0 13 13 0 10 323 10 5498 0 32+40 6 65 .0 5.00 1.33 1 .00 1". 33 1.00 1.00 1. 00 0. 50 0 13 13 0 0 997 0 4502 0 32+7C. . ..66Z..2 5. 0.0__L.33 -L.iL0_ L.33 1.00 1 .00 1 .00 0 .50 0 13 13 0 0 . JL2_ 0 3973 0 33+20 6 7 1 . 1 5.00 5.0G 1. GO 1. 33 1. GO 1. 00 1.0 0 0 . 5 0 0 14 14 0 2 615 2 3360 0 33+70 675 .3 5 .00 5.00 1.00 1.33 1.00 1 .00 l . C O 0. 50 0 14 14 0 243 125 125 3478 0 3 4 + 70 6 8 4 . 7 5.0G 5.0G 1. CO 1. 33 1.00 1 .00 1 .00 0 .50 0 14 14 0 14 47 0 0 4925 0 35+70 6 9 4 . 9 5.00 5.00 1.00 1.33 1. 00 1 . 00 1. 00 0 . 5 0 0 14 14 0 98 1 127 127 5779 0 36+70 7 05 .1 5.00 5 .00 1 .00 1 .33 1.00 1.00 1.00 0 . 5 0 0 14 14 0 611 12 7 127 6264 0 37+7.0 7.1.5.. 4 5. 00 5. 00 1. CO I. 33 1. 00 1 .00 1 .00 0 .50 0 1 3 13 0 966 0 0 7230 0._ 37+79 7 1 6 . 3 5.00 5.00 1.00 1. 33 1.00 1. 00 1. CO 0. 50 0 13 13 0 65 0 0 7295 0 38+70 7 2 5 . 6 5 .00 5 .00 1.00 1 .33 1.00 1.00 1.00 0 . 5 0 0 13 13 0 319 36 36 75 77 0 39 + 70 7 3 5 . 8 5.00 5.00 J-.oo 1. 33 1. 00 1.00 1 . CO 0 . 5 0 0 13 13 0 124 40 40 7662 0 J THESIS PRCJECT, UNIVERS ITY OF BRIT ISH COLUMBIA RESEARCH FOREST; ROAD C CHAINAGE EL EV AT N SLOPES SHRINK SWELL O.M. ROCK DITCH SCRAPER SU8GRADE EXCAVATION F I L L S IDECAST NET BACK CUT F ILL ' DITCH DITCH SLOPE DITCH WIDTHS ACC F ILL RK OM DEPTH DEPTH W I CT H L E F T R IGHT ROCK OM MA SS 40+70 746 .0 5 .00 5.00 1 . 0 0 1 '. 33 1 . 0 0 1 . 00 1. 00 0. 5 0 0 1 3 1.3 0 242 0 0 7904 0 . 41+70 756 . 2 5. 00 5 .00 1.00 1.33 1.00 1 .00 1 .00 0 . 5 0 0 13 13 G 150 27 27 8027 0 42 + 70 7 6 6 . 4 5. 00 5.00 1.00 1. 33 1. CO 1. 00 1.00 0 . 5 0 0 1.3 13 0 3 4 728 34 7333 0 . 43+.2Q.- 7Xl-..5_ _5_..QXL 5 ..G.Q_L._0.0 1..33 L.D.O 1 .00 1. GO <L.J_fl_ 0 1 3 13 0 1 98? 1 6348 0 43 + 70 7 7 6 . 6 5. 00 5.00 1.00 1. 33 1.00 1 .00 1 .00 0 .50 0 13 13 0 0 1761 0 45 87 0 44+20 7 8 1 . 8 5.00 5 .00 1.00 1. 33 1. 00 1.00 1. GO 0.5 0 0 13 13 0 8 1306 8 3289 0 44+70 7 86 .9 5.00 5 .00 1.00 1.33 1.00 1.00 1.00 0 .50 0 .13 13 0 110 '181 110 3218 0 45 + 70 7 9 7 . 1 5. 00 5 .00 1.00 1. 33 1. 00 1.00 1.00 0 .50 0 14 14 0 512 4 4 3725 0 46+70 8 0 7 . 3 5.00 5.00 1.00 1.33 1. 00 1.00 1. 00 0, 50 0 14 -14 0 1127 0 0 4852 0 47+70 ._ _1_._? 5....0.Q 5..D.G 1...Q0 1...3.3 L..0.0 1„CL0 1_, 0.0 0 . 3 0 0 14 14 0 L2X1 0 0 6063 0 48+70 8 2 3 . 0 5.00 5.00 1.00 1.33 1. 00 1.00 1 . GO 0 . 5 0 0 15 1.5 0 392 414 392 6042 • 0 49 + 70 830 .7 5.00 5.00 1.00 1. 33 1. 00 1.00 1. CO 0. 50 0 1 5 15 0 0 2910 0 3132 0 50+70 8 3 8 . 5 5. 00 5 .00 1.00 1 .33 1 .00 1 .00 1 .00 0 .50 0 15 15 0 0 4 055 0 -924 0 51+70 8 4 6 . 3 5.00 5.00 1.00 1. 33 1. CO 1. 00 1. 00 0 . 5 0 0 15 15 0 35 1890 35 - 2 7 7 8 0 52 + 70 8 54 .1 5.00 5 .00 1.00 1.33 1.00 1.00 1.00 0 . 5 0 0 1 5 15 0 226 331 226 - 2882 0 . . 5.3+70. ... . . 86X. 8 5.. 0.0 1... 3.3 1.. 0.0 1.3.3 1.00 1 .00 1 .00 0 .50 0 13 13 c 191 1488 191 -41 79 .0 54 + 20 8 6 5 . 7 5.00 1.33 1.00 1.33 1. 00 1. 00 1. 00 0. 50 0 13 13 0 0 1032 0 - 5 2 1 1 0 54+7 0 8 6 9 . 7 5. 00 1.33 1.00 1 .33 1.00 1.00 1.00 0. 50 0 13 13 0 28 300 28 -5483 0 55+70 8 8 0 . 4 5. 00 1.33 1.00 1. 33 1. 00 1.00 1.00 0 . 5 0 0 13 13 0 56 627 56 - 6 0 5 3 0 56+7 0 891 .4 5.00 1.33 1.00 1.33 1. 00 1.00 1. CO 0. 50 0 13 13 0 2294 602 602 -436.1 0 57+70 9 0 2 . 4 5.00 1.33 L O O 1.33 1.00 1 .00 1.00 0 . 5 0 0 13 13 0 3702 0 0 -659 0 . . . . 5.8 + 7.0. . _ 9 1 3 . 3 5.00 _L._3 1. 0.0 _1..2L3 1. 00 1 . 0 0 1 . 00 0 . 3 0 0 13 13 0 2768 0 0 2109 ... .0. 59+70 9 2 4 . 3 5.00 1.33 1.00 1. 33 1.00 1 .00 1. 00 0. 50 0 1 3 13 0 2443 0 0 45 52 0 60+70 9 3 5 . 3 5. 00 1.33 1.00 1. 33 1.00 1 .00 1 .00 0 .50 0 13 .13 G 12 50 337 3 37 5465 0 61+70 9 46 .3 5.00 1.33 1.00 1. 33 1. 00 1.00 1. 00 0. 50 0 15 15 0 365 618 365 5212 0 62 + 70 9 5 7 . 2 5.00 1.33 1.00 1 .33 1 .00 1 .00 1.00 0 . 5 0 0 15 15 0 204 1017 204 4399 0 63 + 70 9 6 8 . 2 5. 00 1.33 1.00 1. 33 1. 00 1.00 1.00 0 .50 0 15 15 0 380 835 380 3943 0 64+20. . 9 7 3.7 5..JX0 5._0.0 1..00 1. 33 . L-JQJ3 L. 0.0 L. GO Qjf 5 C 0 15 15 0 416 53 5 3 43Q6 ... 0 64+70 ' 9 7 9 . 2 5. 00 5 .00 1.00 1 .33 1 .00 1.00 1.00 0 .50 0 15 15 G 6 23 4 4 4926 0 65 + 20 9 8 3 . 7 5. 00 5 .00 1.00 1. 33 1. GO 1. 00 1.00 0 . 5 0 0 15 15 0 500 213 213 5212 0 65+70 986 .5 5.00 5 .00 1.00 1. 33 1. 00 1.00 1.00 0. 5C 0 15 15 0 159 527 159 4844 0 66+20 9 8 8 . 2 5. 00 5.00 1.00 1.33 1.00 1 .00 1 .00 0 . 5 0 0 15 15 0 82 53 8 82 4389 0 66+70 9 89 .9 5.00 5 .00 1.00 .1 • 33 1. CO 1.00 1. 00 0 . 5 0 0 15 15 0 40 454 40 3975 0 . 6.7_±2.0_„ 9_ai_..6_. _5...0JO_ JL..O-0_L..OJO 1.33 L .00 1 .00 1 . 00 0..3 0 0 1 5 1 5 0 1 1 537 11 3449 _ 0 . 67 + 70 9 9 3 . 2 5. 00 1.33 1.00 1.33 1. GO 1 .00 1 .00 0 .50 0 13 13 0 0 716 G 2733 0 68+20 9 9 4 . 9 5.00 1.33 1.00 1.3 3 1. GO 1.00 1. 00 0. 50 0 13 13 0 0 845 0 1888 0 68+70 9 9 6 . 6 5. 00 1.33 1.00 1.33 1 .00 1.00 1.00 0. 50 0 13 13 0 1 68 8 1 1202 0 69+70 9 9 9 . 9 5. 00 1.33 1.00 1.33 1. 00 1.00 1.0 0 0 . 5 0 0 13 13 0 184 551 184 835 0 70+70 1003 .3 5.00 1.33 1.00 1. 33 1. 00 1. 00 1. CO 0. 5 0 0 13 1.3 0 459 48 48 1246 0 ... . ... .70+9.5. . ..__0JD4.._ _5..J0.O_ _L.33_L._0.Q_. 1..33 1.00 1.00 1 .00 0 .50 0 15 15 0 258 0 0 15.03 . ... 0 . 71+45 1 0 0 5 . 8 5.00 1.3 3 1.00 1. 33 1. 00 1. 00 1. 00 0 . 5 0 0 1.5 15 0 819 0 0 2323 0 71+95 1 0 0 7 . 4 5.00 1.33 1.00 1.33 1.00 1.00 1.00 0 .50 0 15 15 0 1204 0 0 3527 0 72 + 45 1 0 0 9 . 1 5. 00 1.3 3 1.00 1. 33 1 . 00 1 .00 1.00 0 .50 0 15 15 0 1463 0 0 49 90 0 72+74 1010 .1 5.00 1.33 1.00 1. 33 1. CO 1.00 1. 00 0, 50 0 1 5 15 0 868 0 0 5858 0 72 + 95 1 0 1 0 . 8 5 .00 5.00 1.00 1 .33 1.00 1.00 1.00 0 . 5 0 0 13 13 0 508 0 0 6366 0 . 74+50_.. ._ 1.016.0 _5..J3_0_ _5_._0_0_L._OJO_ _ X . 3 3 _ —L..00 L..O.0 1 .00 _0 .50 0 _1_3 13 0 1 275 256 256 73 85 0 75+50 10 20 . 7 5.00 5.00 1.00 1. 33 1. 00 1. 00 1. GO 0. 5 0 0 13 13 0 0 1568 0 5817 0 76+50 1027.1 5. 00 5 .00 1.00 1 .33 1.00 1 .00 1.00 0 .5 0 0 13 13 0 0 2 711 0 3107 0 77+50 1 0 3 4 . 8 5.00 5.00 1.00 1. 33 1. 00 1. 00 1 . GO 0 , 5 0 0 13 13 0 0 1757 0 1349 0 78+50 1042 .5 5.00 5.00 1.00 1.33 1. 00 1. 00 1.00 0 . 5 0 0 14 14 0 0 3 247 0 - 1898 0 79+50 1 0 5 0 . 2 5. 00 5 .00 1.00 1.33 . i . o o 1 .00 1 .00 0 .50 0 14 14 0 337 2798 337 -43 5 8 0 .. 80+00 . . _10_5_4_._1_. _L.J_L 1_. 33_1 . 00 1. 33 1. GO 1.00 1. 00 0, 50 0 14 14 0 619 0 .0. _-.3X3.9 .0 80+5 0 1 0 5 8 . 0 5.00 1.33 1.00 1.33 1.00 1.00 1.00 0 . 5 0 0 14 14 0 1185 0 0 - 2 5 5 4 0 81 + 00 1 0 6 1 . 8 5. 00 1.33 1.00 1. 33 1 .00 1 .00 1.00 0 . 5 0 0 14 14 0 1043 0 0 -1511 0 81 +50 1065 .7 5.00 5.00 1.00 1. 33 l . CO 1.00 1. GO 0, 5 0 0 1 3 13 0 448 28 28 - 1091 0 / CHAINAGE ELEVATN SLOPES SHR INK SWELL O.M. ROCK DI TCH SCRAPER SUBGRADE EX CAV AT I ON F I L L S IDECAST NET BACK CUT F I L L DITCH DITCH SLOPE DITCH WIDTHS ACC F I L L RK OM . DEPTH DE PTH WI DTH LEFT P IGHT ROCK OM MA SS 82+00 1069.6 5.00 5 .00 1.00 1 .33 1.00 1.00 1.00 0.50 0 13 13 0 245 3 5 35 -8 81 0 , 82+50 1C73.4 5. 0 0 5. OC 1. 00 1.33 1 . 00 1 .00 1.00 0 .50 0 13 13 0 166 7 7 -721 0 N 83+00 1077.3 5. 00 5.00 1.00 1.33 1.00 1.00 1. CO 0. 5 0 0 13 13 0 18 1 0 0 -541 C . 83+50 . ..._.ljG..ai...2._._ ._5.._0.0_ 5 .0.0 1 .00 _ L . 3 3 1 .00 1 .00 1. 00 0.50 0 1 3 13 0 205 48 48 • -3 84 . _ . Q 84+50 1088.9 5.00 1.33 1. 00 1. 33 1.00 1.00 1 .00 0.50 0 15 15 0 522 215 215 -77 0 8 5 + 50 1095 .8 5.00 5 .00 1.00 1. 33 1. 00 1. 00 1. 00 0.50 0 15 15 0 1042 119 1 19 847 0 86+00 1098.4 5. 00 5. 00 1.00 1.33 1 .00 1 .00 1 .00 0 .50 0 15 15 0 43 9 0 0 1286 0 8 6+5 0 1100 .3 5.00 5 .00 1. 00 1. 33 1. CO 1. 00 1. 00 0.50 0 15 15 0 99 128 99 1257 0 87 + 00 1 101 .7 5.00 5 .00 1.00 1.33 1.00 1.00 1.00 0. 5 0 0 1 5 15 0 6 369 6 895 0 _ -. 8 7+5 0. 1.10.2. A__ _5.._0X_ .5.00 . .1.._<L0_ 1. 33 1 .0.0 J.....00 1 .DO 0 .50 0 15 15 0 0 430 0 ____6J5„. 0 88+00 110 2.7 5.00 5.00 1. 00 1.33 1.00 1 . 00 1. 00 0. 50 0 15 15 0 1 488 1 -23 • 0 88+50 1102.9 5.00 5.00 1.00 1 .33 1.00 1.00 1.00 0. 50 0 15 15 0 40 530 40 -512 0 89+00 1103.1 5. 00 5. 00 1. 00 1. 33 1. 00 1 .00 1.00 0.50 0 15 15 0 131 259 131 -640 0 89+50 110 3.3 5.00 5 .00 1.00 1. 33 1.00 1.00 1. GO C. 50 0 15 15 0 350 2 8 28 -318 0 90+ 50 1103.7 5. 00 1 .33 1 .00 1 .33 1.00 1 .00 1.00 0.50 0 1 3 13 0 1717 0 0 13 99 0 91 + 00_. _11_C3_._9.__ __5_..0.0_. _1..33_ _1.._Q_0_ 1. 33 1. CO 1 . 00 L. 0_0 0_..5D 0 13 13 0 869 • 0 0 ...22.68 . .... 0_ 91 + 50 1104 .1 5.00 5 .00 1.00 1. 33 1.00 1 .00 1.00 0.50 c 13 13 0 289 60 60 2497 0 92 + 00 1104.3 5. 00 5. 00 1.00 1.33 1. 00 1 .00 1 .00 0.50 0 13 13 G 50 99 50 2448 0 92+50 1104.5 5.00 5.00 1.00 1. 33 1. 00 1 .00 1. 00 0, 50 0 13 13 0 9 3 57 57 2483 G 93 + 50 1105.0 5.00 1.33 1 .00 1.33 1 .00 1 .00 1.00 0.50 0 13 13 0 569 37 37 3016 0 94+00 1105.2 5. 00 1. 33 1. 00 1. 33 1.00 1 .00 1.00 0 .50 0 13 13 0 321 37 37 3301 0 94 + 50 .. l l j O „ . J L _ _5_._0_0_ 1.33 1.00 L. 33 1.00 1. 00 L» 0_0 0. 50 0 13 13 0 L14 206 114 3208 0 95+00 1105.6 5. 00 1 .33 1 .00 1 .33 1.00 1.00 1.00 0.5 0 0 13 13 0 14 4 87 14 2735 0 95 + 50 1105.8 5. 00 1.33 1. 00 1.33 1. 00 1.00 1.00 0.50 0 13 13 0 0 7 73 0 1962 0 96 + 00 1106 .1 5.00 1 .33 1.00 1. 33 1. 00 1. 00 1. GO 0.50 0 1.3 13 0 0 922 0 10 40 0 96+12 1106.2 5. 00 1.33 1.00 1.33 1 .00 1 .00 1.00 0 .50 0 13 13 0 0 243 0 797 0 96+41 1106.8 5.00 1.33 1. 00 1. 33 1. 00 1. 00 1 .00 0. 50 0 13 13 0 0 691 0 106 0 97.+00._ 1.1_Q.8_..6_ _5_.J_-.0_ _L..33_ _1_.JO.0_. 1.33 1 .00 1 .00 1 ,.0.0 0.50 0 _JL3 13 0 0 L0.23 0 -9 17 ... o 97+50 1110.2 5. 00 1. 33 1. 00 1. 33 1 .00 1 .00 1 ,00 0 . 50 0 13 13 0 115 221 115 -1023 0 98+50 1113.4 5.00 1.33 1.00 1.33 1.00 1.00 • l . o o 0, 50 0 13 13 0 476 0 0 -547 0 99+50 1116.5 5. 00 1 .33 1 .00 1 .33 1 .00 1.00 1.00 0.50 0 13 13 0 9 61 0 0 414 0 100+50 1119.7 5. 00 1. 33 1. 00 1. 33 1. 00 1.00 1 .00 0.50 0 13 13 0 1209 0 0 1623 0 IH E 3.3.01 __Z.E RO D.I_VXD.E._I.N._S_T_A_L£MJ±NJ^ EXECUTION TERMINATED INVALID COMMAND SSIGNOFF AP?-T(Qt)|X _ UKJ-AP ?\UD(__TIAMH\H(\ A LX-O CA-~f\ t) M  EXECUTOR. MPS/360 V2-M8 PAGE 1 - 70/331 CONVERT VOLALOC TO PBFILE TINE = 0.03 SUMMARY CHECK 1- ROWS SECTION. 0 MINOR ERROR(S) - 0 MAJOR EFPOP ( S ) . _ ^ c d UJKNS S E CTTO N~. ' ~ ~ ; " 0 MINOR ERROR IS) - 0 MAJOR EPROR(S). 3- RKS'S SECTION.  TOTVOA 0 MINOR E RROR(S> - 0 MAJOR EPROP(S). NUMBER OF ELEMENTS BY COLUMN ORDER 69 F C 5 0 C 0 2 0 . F 0 5 0 C 0 3 0 . 76 F C 5 C C 0 9 0 . F 05C8ORR. 83 F 0 5 5 C 0 8 0 . .3 F055CO85. F 0 5 5 C 0 9 0 . . . • • 3 2 7 3 ^ 90 F 0 6 0 C 0 4 0 . F06OCO7O. 3 3 97 F 1 0 0 C 0 3 5 . F 10CC040. F 1 0 0 C 0 8 0 . . . 9 9 3 1 04 F100C160 . • • • . 3 F 1 0 0 C 1 6 3 . 3 111 F 110C085. F 1 1 0 C 0 9 0 . 3 118 F 1 2 0 C 0 7 0 . F12GCC80 . F 1 2 0 C G 8 5 , . . * . 3 -a 125 F 1 2 0 C 1 / 0 . F120B0RR. . .3 132 F 13 OC 160. F 1 3 GC 16 3. 139 F132C090 . 9 0 * .3 F13 2 C 1 5 7 . 9 9 9 . 3 F 1 3 2 C 1 6 0 . . . 9 . 3 146 F 1 3 6 C 0 8 0 . - F 1 3 6 C 0 8 5 . 153 F136B0RR . 2 F 14CC070. 160 F140C163 . • • * .3 F140C 170'. •> 167 F 1 5 0 C 1 6 0 . F 1 5 0 C 1 6 3 . 174 F 1 8 0 C 1 6 3 . F 18CC 170. -> F 1 8 0 C 2 2 0 . . . 9 .3 3 181 F 1 8 3 C 1 6 0 . F 183C163. 1 88 F 18 3B0RR. F 1 8 9 C 1 5 7 . • • 9 .3 195 F 1 8 9 C 2 4 7 . F 1 8 9 C 2 5 1 . * • « F 189C257. 0 . 3 3 202 F3.90C170, F 1 9 0 C 2 2 0 . _ 209 F 2 0 0 C 1 5 7 . -i F 2 0 0 C 1 6 0 . F 2 0 0 C 2 4 7 . . . . . 3 216 F200C251 . 9 9 9 .3 F20OC257 . * A • . 3 F 2 0 0 C 2 6 7 . . . 9 . 3 2 23 F 2 1 0 C 1 7 0 . • • • .3 F 2 1 0 C 2 2 0 . 230 F 2 1 0 C 2 7 7 . -a F21CB0RR. 237 F297C277 . F 2 9 7 C 2 8 7 . 244 F 2 9 7 C 3 4 7 . F 2 9 7 C 3 5 7 . . . .3 2 51 F 3 1 7 C 2 6 7 . F 3 1 7 C 2 7 7 . 258 F 3 1 7 C 3 3 7 . F 3 1 7 C 3 4 7 . . .3 265 F317B0RR. F 3 2 4 C 2 5 7 . 272 F 3 2 4 C 3 0 7 . * » • .3 F 3 2 4 C 3 1 2 . « 0 _ . 279 F 3 2 4 C 3 7 8 . F 3 2 4 C 3 8 7 . 286 F 3 2 7 C 2 8 9 . 9 9 9 .3 F3 27C29 5. F 3 2 7 C 3 5 7 . . . . . 3 2 93 F327C367 . « * 9 .3 F 3 2 7 C 3 7 7 . 9 9 9 .3 300 F 3 3 2 C 2 7 7 . F 3 3 2 C 2 8 7 . 307 F 3 3 2 C 3 4 7 . F3 32C 35 7. i F 3 3 2 C 3 6 7 . . . 9 . 3 . .3 314 F332B0RR. F 4 2 7 C 3 5 7 . 321 F427C 407 . F 4 2 7 C 4 1 7 . 328 F 4 3 2 C 3 7 7 . F4 3 2C378. ft 9 * F 4 3 2 C 3 8 7 , 9 . 3 •a 335 F 4 3 2 C 4 6 7 . F 4 3 2 C 4 7 7 . , • 3 342 F43 7C 3 9 7 . F43 7C407. 349 F 4 4 2 C 3 7 7 . 0 4* .3 F 4 4 2 C 3 7 8 . 9 9 9 . 3-356 F 4 4 2 C 4 6 7 . F 4 4 2 C 4 7 7 . •363 F 4 4 7 C 4 0 7 , F 4 4 7 C 4 1 7 . 370 F487C457 . 9 9 9 .3 F 4 8 7 C 4 6 7 . t> 9 • . 3 377 F49780RR . F50 rC4> f . 384 WASTC0 3 5 . WASTC040. WASTC 070. . . * . 2 W A S T C 0 8 0 . . . . .2 391 WASTC160. WASTC163. 398 WASTC257. WASTC267. 405 WASTC 31 2. * * « .2 WASTC337. 9 9 9 . 2 W A S T C 3 7 5 . . . . . 2 412 WASTC387. WASTC397. EXECUTOR. MPS/360 V2-M8 PAGE 3 — 70 /331 •\ NUMBEP OF ELEMENTS 8Y ROW ORDER, EXCLUDING RHS ' S , INCLUDING SLACK ELEMENT 1 N VQLACO . . . 351 E 02 + 00C '. . . . . 5 E 03+OOC E 03+50C 6 E 04+00C E 07+COC . . . . 1 2 E 0 8+00C . . . . 1 3 8 E 08+50 C . . . .13 E 09+00C . . . . 13 E 15+73C . . . .16 E 16+OCC . . . .16 E 16+34C . . . .16 E 17+00C . . . .16 E 2 2+00C / 15 E 23+70C . . . . . 9 E 24+70C . . . .10 E 25+15C E 2 5+70C . . . . 10 E 26+70C . E 2 7+70C ...... 8 E 28+70C S 22 E 28+77C . . . . .7 E 29+52C . . . . . 7 E 30+70C E 31+24C . . . . ,7 E 33+70C . E 34+70C 7 E 3 5+70C 29 E 36+70C . . . . 10 E 37+70C . ...H E 37+79C . . . . 11 E 3 8+7 0C . . . . 11 E 39+70C . E 40+70C . . . . .7 E 41+70C 36 E 45+70C . . . . 10 E 46+70C . . . . 1 0 E 47+70C . . . .10 E F05+00 . . . . 10 E F05+50 . . . . 10 E F06+00 . . . . 1 0 E F10+00 . . . . 1 3 43 E F l l + O O . . . . 11 E F12+00 . . . . 1 0 E F 13+00 . . . . 10 E F13+20 . . . .10 E F13+6 7 . . . .10 E F14+00 . . . . 1 0 E F15+00 . . . . 10 50 E F1 8+0 0 9 E F18+31 . . . .10 E F18+90 .... 11 E F.19+00 . . . . 11 E F20+C0 . . . . 12 E F21+0 0 . . . .13 E F29+70 . . . . 1 7 57 E F31+70 . . . . 19 E F32+40 . . . . 1 7 E F32+70 . . . . 18 E F33+20 . . . . 1 7 E F42+70 . . . . 13 E F43+20 . . . . 1 2 E F43+70 . . . . 1 2 64 E F44+20 . . . . 1 1 E F44+70 . « • 9 1 1 E F48+70 E F49+70 5 E F50+70 . PROBLEM S T A T I S T I C S - 68 ROWS, 418 VAR IABLES , 1051 ELEMENTS, DENSITY = 3 .69 THESE S T A T I S T I C S INCLUDE ONE SLACK VARIABLE FOR EACH ROW.  0 MINOR ERRORS, 0 MAJOR ERRORS. EXECUTOR. MPS/360 V2-M8 I PAGE 4 - 70 /331 SETUP P B F I L E TIME = 0 . 4 3 MIN < MATRIX1 ASS IGNED TO MATRIX. MATRIX2 ASSIGNED TO MATRIX 2 ETA 1 ASSIGNED TO ETA1 ETA 2 ASSIGNED TO ETA2 SCRATCHl ASSIGNED TC SCRATCHl SCRATCH2 ASSIGNED TO SCRATCH 2 MPS C RAT ASSIGNED TO MPSCRAT MAXIMUM PRICING NOT REQUIRED - MAXIMUM POSS IBLE 5 NO CYCL ING POOLS NUMBER S I ZE CORE  H .REG-B ITS MAP 2 84 WORK REGIONS 7 5 68 39 76 MATRIX BUFFERS 3 6728 20184  ETA BUFFERS 5 35 04 17520 TOTAL NORMAL . F R E E . F IXED BOUNDED ROWS ( L O G . V A R . ) 68 0 1 67 0 COLUMNS ( S T R . V A R . ) 350 350 0 0 0 1051 ELEMENTS - DENSITY = 3 .69 - 3 MATRIX RECORDS (WITHOUT RHS ' S ) P ICTURE - USING P B F I L E T IME = 0 .51 i x r H CO O CM t — ix r H oo o o r\i ro r- r-i x i — 1 co o u CM M o 1— LL -H CO a u r - t o t-IX T—1 oo o _ i — 1 ro (— LL r-i CO o o r H •o O r-LX r - l 00 o o r - l _ ^ Is- 1— IX i — 1 i n o co a cc y~ IX. r-i i n o <_ rvi r\l o r -i x r-i i n o a r—1 o t -IX r - l m o r H _ ro t -LL r - l i n o w r-t o o r — IX r - l m o o r-i i n r— h-u. r~t i n o o o o- o r -LL r-i i n o <j> o co m r -LL r-t i n o o O CO _ r— IX r-t <r o a _ _ I-U, r-i >r o _ r H o t— IX r-i -sT O u r H ro t— IX r-t -T O l_) r—1 sO a r — IX r - l <r o a r H in I s- f-IX r - t o o O a-- c . h-I X r-i o _ O co i n K i x - t <r o u O 00 o r -LL r-< sT o o o O r -IX r H m CO c _ t _ IX r H r o _ l_> r H o H IX r - l ro o r - l ro t ~ IX r—1 CO o r H _ o r -IX r - l ro _ r H i n r ~ t -IX r - l ro _ u o a o t -IX —-1 r o o o o oo i n r — IX r - l ro o o oo a r -IX r—1 m o o r - o r -IX I—1 r o f \ J CO o cx r -L L r - l ro CM l_> r H r- o r— L L r - l ro <M o r H *c r o k-L L r o fx) o r-i •o o h-IX r - l r o CM (_> r—i n r- r — IX r - l ro CM u o cr- o J — IX r - t r o CM l_> o co i n r— a . r-i CO CM o o co o r— IX r-i r o CM l_) o r - o r -u_ r-i r o _ cu O c_ cc t— L L r-i r o o (_> r H r - o' t— L L r - t r o o u r H O r o r -L L r—i CO o o r H _ o r -IX r ~ ! r o o o r - t m I s- r — IX r - t r o o _ o t r o r — IX r - t r o o l _ o CO m t— L L r - t r o a o o CO o i — L L r - l r o o o o 1— o r — L L r - l r \ i o CO o C t IX t -L L r - t o o r H r - o f— L L r - t ( M O O r - t „ r o o u u o o <t o o _ l + + o CM ro > o o 2! UJ IX! 1X1 LU LU LU IX1 UJ u u u o o o in o o + + + n >t r~-o o <-> U vJ o c o o O IT . O + + + CO CD CP o o a _ <_ u m o <r r- o ro + + + in vo _ _•<__> o o a o o r-+ + + P— f\j ro r-t r\j r\j O o o o w\ o r - r-i r-+ + + s j - m _^ rsj rvi CM LULLi _ L L ' _ U J _ l X I U J U J l _ L U U J _ o o o r - r - f -+ + + _ f - co 0. CM CM O O O r- CM o r- wo r-+ -f + oo o> o CM <M ro o o u sfr c o <\j r~ r~ • + + r-t ro V t co ro ro O O _ O O O r~ r- r-+ + + i n o r-ro r " ro u u u c o o r«- r- r~ + + + M X ) ro ro ro O O o O C O r- r - r-+ + + O r - l i n <r v j -U J L U U J I X l L U U J l — U _ _ L U l _ _ L U L U _ U LULU O l_> O O O O p» r- + + + -n _ r- o •<t <r u-o c in o + + in _ o o I X L L O O O O o o + + + r H (N rO r H r H r H U - L L I X o r» rsj _ •t- + ro ro F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 2, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3 2 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 6 6 6 6 6 6 6 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C C B C C C C C C C C B C C C C C C C C B C C C C C C C C B C C C C C C C C B C C C C C C C C B C C C C C C C 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 2 0 1 1 1 1 2 2 2 . 6 7 ,R 7 8 8 9 5 6 6 7 R 7 8 8 9 5 6 6 7 R 7 8 8 9 5 6 6 7 R 7 8 8 9 5 6 6 7 R 8 8 9 - > 6 6 f 2 R 5 6 6 7 2 3 4 ^ 3 0 R 0 0 5 C 7 0 3 0 R 0 0 5 0 7 0 3 0 R 0 0 5 0 7 0 3 0 R 0 0 5 0 7 0 3 0 R 0 5 0 7 0 3 0 0 R 7 0 3 0 0 7 7 ~F14+00 E ~ l " l 1 1 1 1 1 1 1 F15+00 E 1 1 1 1 1 1 1 1 1 F18+00 E F18+31 T F 18+90 E F19 + 00 E F20+00 E F21+00 E F29+70 E F31+70 E F32+4C E F32+70 E F33+20 E F42+70 E F43+20 E F43+70 E F44+20 Ff F44+70 E F48+70 E F49+70 E F50+70 E 1 1 1 1 1 1 1 F F F F F F F F F F F F F F F F F F P F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 8 8 8 8 - 6 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 9 9 0 3 3 3 3 2 3 3 3 3 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 O O 0 0 O 0 0 0 0 O 0 0 0 7 7 B C C C C C C C C B C C C C C C C C C B C C C C C C C C C B C C C C C C C C C C B C C C C C C C C C C C B C C 0 1 1 1 1 2 2 2 2 0 1 1 1 1 2 2 2 2 2 Q 1 1 1 1 2 2 2 2 2 0 1 1 1 1 2 2 2 2 2 2 0 1 1 1 1 2 2 2 2 2 2 2 0 2 2 5 6 6 7 2 3 4 5 5 6 7 R 5 6 6 7 2 3 4 5 R 5 6 6 7 2 4 5 5 R 5 6 6 7 2 3 4 5 5 R 5 6 6 7 2 3 4 5 5 6 R R 3 4 R 7 0 3 0 0 7 7 1 R 7 0 3 0 0 7 7 1 7 R 7 0 3 0 0 7 7 1 7 R 7 0 3 0 G 7 7 1 7 7 R 7 0 3 0 0 7 7 1 7 7 7 R 7 7 VOLACO M T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T 02+000 E 0 3+C0C E 03+5OC E 04+00C E 07+OOC F 08+OOC E 08+50C c 09+OOC E 15+73C E 1 1 1 1 1 16+00C E 1 1 1 1 1 16+34C E 1 1 1 1 1 17+00C E 1 1 1 1 1 22+00C E 1 1 1 1 1 2 3+7CC E 1 1 1 1 1 1 24+70C F 1 1 1 1 1 1 25+15C E 1 1 1 1 1 2 5+70C E 1 1 1 1 26+70C E 1 1 27+70C E 1 28+70C E 28+77C E 29+52C E 30+70C F 31+24C E 3 3+70C E 34+70C F 35+70C E 36+ 70C E 37+70C E 37+79C E 38+70C E 39+70C E 40+70C E 41+70C E 45+70C E 46+70C E 4 7+70C E F05+00 p F05+50 E F06+00 E F10+00 E F l l + O O F F12+00 E F13+00 E F13+20 p F13+67 c F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 5 5 5 5 5 5 5 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C C C C C C C C e C C ' C C C C C C B C C C C C C C C B C C C C C C C C ' C C C B C C C C C C C C C B C C C C C C 0 0 0 0 0 0 0 0 0 O C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 2 3 3 4 7 8 8 9 R 2 3 3 4 7 8 8 9 R 2 3 3 4 7 8 8 9 R 3 3 4 7 8 8 9 5 6 6 7 R 4 7 8 8 9 i > 6 6 f R 7 8 8 9 5 6 0 0 5 0 0 0 5 0 R 0 0 5 0 0 0 5 0 R 0 0 5 0 0 0 5 0 R 0 5 0 0 0 5 0 7 0 3 C R 0 0 0 5 0 7 0 3 0 R 0 0 5 0 7 0 " V O L ACO N~~^n~l T T T T T T " ~ T T T T T T 7 T T T T T T 7 T T T T T T J~~J~T T T T I " T T T T T T T T T T T T T T T ~ " T T T T" 02+00C F 1 1 1 03+0CC E 1 1 1 1 03+50C E l 1 1 1 04+00C E l 1 1 1 1 07+0OC F 1 1 1 1 1 1 08+00C E l 1 1 1 1 I 08+500 E l 1 1 1 1 1 09+00C E 1 1 1 1 1 1 15+7 3C E ; : I I I 16+00C E 1 1 1 16+3AC E 1 1 17+00C E 22+00C E 23+7CC E 24+70C E 25+15C E 25+70C E 26+70C E 27+70C E 28+70C E 28+77C E 29+52C E 30+70C E 31+24C E 33+70C E 34+70C E 35+70C E 36+70C E 37+70C F 3 7+79C E 38+70C E 39+7CC E 40+70C E 41+70C E 45+7CC E 46+70C E 47+70C E FQ5+00 E 1 1 1 1 1 1 1 1 1  F05+5 0 E 1 1 1 1 1 1 1 1 1 F06+00 E 1 1 1 1 1 1 1 1 1 F10+00 E 1 1 1 1 1 1 1 1 1 1 1 1 Fll+OO E 1 1 1 1 1 1 1 1 1 1 F12+00 E F13 + 00 E  1 1 1 1 1 1 ( S i LL <—1 c\j O o rH •o o LL l-t <M O u rH t\ r -LL I - l CM O u o cr> o IX —t CM O o o OO i n IX rH CM o u o oo O LL rH CM o o o *- o LL f H 1—1 o CO o _ cc IX r-l rH o _ rH o IX f-H rH o o H ro LL rH I-H o o rH _ o U, rH) rH o o rH r -IX. rH r-1 o u o IX i — i !—1 o <_) o CO i n ix. i—I i — 1 o o o co _ IX. r—1 !-» o u o u. i—1 rH o u o o- o IX rH o O CD o C- cc IX rH o o o rH r- o IX rH o O o rH o ro LL rH o o o rH -o o U. rH1 ' o o o in r -tx -Hi o o l_> o (?> o u. —H o o o o oo i n IX •H o o <J o CO O IX. rH o o o o r- O tx f-f o o _ o -J- O u. •—! o o u o ro i n i x H o o o o ro o u. o o CD o cc cc u. o o o o o u_ o o o o oo i n i x o o u o 00 o i x o o o r» o i x o o o u o o tx o o _ o rn i n IX. o sO o l_) ro o i x o o _ o CM o IX, o i n i n CD o c_ cc i x o i n m o o o u_ o u\ m o o 3D i n u_ o i n i n _ o oo o IX c i n m o r- o IX o m _ o <f o IX o m i n o o ro i n IX O i n i n o o ro _> IX O m i n l_> o o LX o in- o CD o cc cc IX o i n o _ o c IX o m c o o CO m IX o m o l_> o 00 o IX o i n o _ o o IX o i n o o o IX o i n o o o ro i n IX o m o o o ro o u» o in. o u o rvj o UJ UJ LU O O O o o o + + + st- m oo rH rH rH IX IX LL o o ro o + 4-CO 03 -U - I X I X o o o o o r -+ + + o - t cr-M N M O O O r - sr r -+ + rM r\i ro ro ro IX IX IX L U L U L U L U L U O J U J m L U L X i L U U j L U U J L U U J U J L U o o o r\i r~ rv + + + ro CM cn ro - r <r IX LX U-o o o r - C\J r~ + + + ro * r sr St- "T >3" LL- LL IX O O O r-. r -+ + + co o sr <r i n LL LL IX ro CM IX CM r - u CM 4- r -IX CM o> r» l_> CM r o r -IX CM r H o CO o sc c_ U- CM rH o O CM *- r~ IX. 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CM o o o CM m r-t LL CM o o _ CM •X I s-IX CM o o o CM ro r -i x CM o o ( J CM IM o LL CM o o o r H i -~ o u» CM o o o r H vO ro LX CM o c r H •JQ o IX CM o o _ r H m r» IX r H cr o CD CD- cc cc IX r - l o _ CM m r-IX i—1 Cj> o o CM i n •H IX r H cr- o u CM <r r-IX t—i o o o CM ro r -IX. r H o _ CM CM o IX r H o o rH r~ o LL r H _) _ r H •£> CO IX r H a > o _ r H _ o IX r H cr o <_> r H i n f -IX r H CO CT co O _ cc IX r H 00 0 s o CM m r~ LL H 00 cr- o CM i n —H LL r H 00 cr CM sr r~ IX r H co v> u CM ro r -u . - 1 00 CJ-- <J CM CM c IX —H 00 l_> r H r - o IX t - > 00 - u r H ro IX r H 00 O'- _ r H o tx r H CO er o r H m •r-IX r H 00 ro CD a cc IX. r H 00 ro u CM i n r H IX r - l CO CO CM r~ IX r H 00 ro o CM ro r -IX r H CO ro o CM CM o IX r~t oo CO _ r H c IX r H oo ro o r H CO IX r H 00 ro o r H _ o IX r H CO ro o r H i n r -IX r H 00 O co O cc cc 1X1 LU UJ O O O o o o + + + sf i n oo r-i ^ U- IX LL. UJ LU LU r H o a ro o + + + cc oo o> r - l rH r - l LL u . 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LU LU UJ r~- -J" r~ + + + r H CM CM ro co ro LL IX IX LL LU LU Xi LU o c r - CM + + CM ro IX LL o o o r - M r -+ + + ro <r <f <r IX LL LL LU LU LU o o o r - r - r -+ + + oo cr o sf «r i n F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 9 9 9 S S 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 7 7 7 7 7 7 7 C C C C C C C C C C C C C B C C C C C C C C C C C C C C C C C B C C C C C C C C C C C C C C C B C C C C C C C 2 2 2 2 2 2 2 3 3 3 3 3 3 0 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 O 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 O 2 2 2 2 2 2 3 5 6 7 8 8 9 0 1 3 4 5 6 R 4 5 5 6 7 8 8 9 0 1 3 4 5 6 7 7 8 R 1 7 7 7 7 5 7 2 7 7 7 7 R 7 1 7 7 7 7 8 5 7 2 7 7 7 7 7 8 7 R 5 6 7 8 8 9 7 7 7 7 8 5 0 1 3 4 5 6 7 7 8 R 5 6 7 8 8 9 0 7 2 7 7 7 7 7 8 7 R 7 7 7 7 g 5 7 V0LAC0 H T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T 02 + 00C E 03+OOC E 03+50C £ 04+00C E 07+00C E 08+00C E 08+50C E G9+00C E 15+7 30 E 16+00C E 16+34C E 17+OOC E 2 2+00C E 23+7 0C E 24+70C E 1 25+15C E 1 1 2 5+7 OC E 1 1 1 1 26+70C £ 1 1 1 1 27+70C E 1 1 1 1 28+70C E 1 1 1 1 28+77C E 1 1 1 1 29+52C E 1 1 1 1 30+70C E 1 1 1 1 31+24C E 1 1 1 33+70C E 1 1 1 34+70C E 1 1 1 35+70C E 1 1 1 36+70C E 1 1 1 37+70C E 1 1 37+79C E 1 1 3 8+70C F 1 1 3 9+70C E 4C+70C E 41+70C F 45+7 0C E 46+70C E 47+70C E F05+00 E F05+50 e F06+0C E F10+00 E F l l + O O E F 12 + 00 E F13+00 E F13+20 E F13+67 F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 2, 4 > 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 _ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 9 9 9 9 c 9 c 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 7 7 7 7 7 .7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 7 7 7 7 7 7 7 C C C C C C C C C C C C C B C C C C C C C C C C C C C C C C C B C C C C C C C C C C C C C C C B C C C C C C C 2 2 2 2 2 2 2 3 3 3 3 3 3 0 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 ;o 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 0 2 2 2 2 2 2 3 J 5 5 6 7 8 8 9 0 1 3 4 5 6 R 4 5 5 6 7 8 8 9 0 1 3 4 5 6 7 7 8 R c 6 1 8 8 9 0 1 3 4 c _> 6 7 7 8 R b 6 7 8 8 0 1 7 7 7 7 8 5 7 2 7 7 7 7 R 7 1 7 7 7 7 8 5 7 2 7 7 7 7 7 8 7 |R 7 7 7 7 8 5 7 2 7 7 7 7 7 8 7 R 7 7 7 7 9 5 7 F14+0G E F15+00 E F18+00 F F18+31 E F18+90 F F19+00 E F20+00 E F21+C0 F F29+70 " E 1 1 1 1 1 1 1 1 1 1 1 1 1 1 F31+70 E 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 F32+40 'E 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 F32+70 c. 1 1 1 1 1 1 1 F33+2 0 E F42+70 E F43+20 E F43+70 FA4+2 0 E F44+70 E F48+70 E F49+70 E F50+70 E F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 7 7 7 7 7 7 7 7 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 7 7 7 7 7 7 7 7' 7 7 7 2 2 2 2 2 2 2 2 2 2 2 7 7 7 7 7 7 C C C C C C C C C B C C C C C C C C C C C C C C C 8 C C C C C C C C C C C B C C C C C C C C C C B C C C C C C 3 3 3 3 3 3 3 3 3 0 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 0 3 3 3 3 3 3 4 4 4 4 4 0 3 3 3 3 3 4 4 4 4 4 0 3 3 3 3 3 4 1 3 4 5 6 7 7 8 9 R 6 7 8 8 9 0 1 3 4 5 6 7 7 8 9 ^ 5 6 7 7 8 9 0 l 5 6 7 R 6 7 7 8 9 0 l 5 6 7 f t 6 / / 8 y o 2 7 7 7 7 7 8 7 7 R 7 7 7 8 5 7 2 7 7 7 7 7 8 7 7 R 7 7 7 8 7 7 7 7 7 7 7 R 7 7 8 7 7 7 7 7 7 7 R 7 7 8 7 7 7 " V O L A G O N " Y ~ J ~ Y ~ T T T T T T T T T T T T T T T T T T T T T T T T T T T T T f T T f T T T T T T T T T T T T T ' T T T T T T C2+00C E • 03-t-OOC E "_ 03+50C E 04+COC E 07+OOC E 08+00C E 08+500 E G9+00C E 15+73C E 16+00C E 16+34G E 17+00C E 22+OOC E 2 3+70C E 24+70C E 25+15C E 25 + 7CC E 26+70C E 1 27+70C E 1 2 8+70C E 1 28+77C F 1 29+ 52C E 1 30+70C E 1 31+24C E 1 1 33+ 70C E 1 1 34+70C E 1 1 35+70C E l 1 1 36+70C E l 1 1 1 1 37+70C E 1 , , 1 1 _1 1 37+79C E 1 1 1 1 1 38+7GC F i l l 1 1 39+70G E 1 1 1 1 1_ 40+70C E 1 1 41+70C F 1 1 45+70C E [ 1 1 46+700 E 1 1 47+70C E 1 1 F05+00 E  F05+50 E F06+00 E F10+00 E  F11+00 E F12+00 E F13+00 E  F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 2, SPj 3 3 3 3 3' 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 7 7 7 7 7 7 7 7 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 7 7 7 7 7 7 7 7 7 7 7 2 2 2 2 2 2 2 2 2 2 2 7 7 7 7 7 7 C C C C C C C C C B C ' C C C C C C C C C C C C C C B C C C C C C C C C C C E C C C C C C C C C C B C C C C C C 3 3 3 3 3 3 3 3 3 0 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 0 3 3 3 3 3 3 4 4 4 4 4 G 3 3 3 3 3 4 4 4 4 4 0 3 3 3 3 3 4 1 3 4 5 6 7 7 8 9 R 6 7 8 8 9 0 1 3 4 5 6 7 7 8 9 R 5 6 7 7 8 9 0 1 5 6 7 R 6 7 7 8 9 0 1 5 6 / R 6 7 7 8 9 0 2 7 7 7 7 7 8 7 7 R 7 7 7 8 5 7 2 7 7 7 7 7 8 7 7 R 7 7 7 8 7 7 7 7 7 7 7 R 7 7 8 7 7 7 7 7 7 7 R 7 7 8 7 7 7 F14+00 E ' F15+00 E F18+00 E  F18 + 31 E F18+90 E F19+00 . _F , , F20+00 E F21+00 E F29+70 E  F31+70 E F32+40 E F32+70 E 1 1 1 1 1 1 1 1 1 1  F33+20 E 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 F42+70 E 1 1 1 1 1 1 1 1 1 1 1 1 F43+20 E 1 1 1 1 1 1 1 1 1 1 1 F43+70 E F44+20 E F44+70 E  F48+70 E F49+70 E F50+70 E 1 1 1 1 1 1 F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F f c k W W W W W W W . W W W W W W W W It 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 A A A A A A A A A A A A A A A A A 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 8 8 8 8 9 9 9 9 0 0 0 0 S S S S S S S S S S S S S S S S S 7 7 7 7 7 2 2 2 2 2 2 2 2 2 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 T T T T T T T T T T T T T T T T T C C C C B C C C C C C C C C B C C C C C C C C C B C C C C B C C C B C C C B C ' C C C C C C C C C C C C C C C C 4 4 4 4 0 3 3 3 3 4 4 4 4 4 0 3 3 3 3 4 4 4 4 4 0 4 4 4 4 0 4 4 4 Q 4 4 4 G 0 0 0 0 0 0 0 0 1 1 1 1 2 2 2 2 2  1 5 6 7 R 7 7 8 9 0 1 5 6 7 R 7 / 8 9 0 1 5 6 7 R 1 5 6 7 R 5 6 7 H 5 6 7 R 2 3 3 4 7 8 8 9 5 6 6 7 2 3 4 5 5 7 7 7 0 R 7 8 7 7 7 7 7 7 7 R 7 8 7 7 7 7 7 7 7 R 7 7 7 7 R 7 7 7 R 7 7 7 R 0 0 5 0 0 0 5 0 7 0 3 0 0 7 7 1 7 " V C JTA C O N T T T ~ T T T T T T T T T T~T T T T - T T T T T T T T ~ f T T T T T T T T 'TT~ I T T T T T T T T T T . T T ~ T T T T T^T 0 2 + 0 0 C E 1 0 3 + 0 0 C E 1 0 3 + 5 0 C E 0 4 + 0 0 0 E 0 7 + 0 0 C E 1 1 1 0 8 + 0 0 C F 0 8 + 5 0 C E 0 9 + 0 0 C E 1 1 1 1 5 + 7 3 C E 1 6 + 0 0 C F 1 6 + 3 4 C E 1 1 1 17+00C E 22+OOC E 23+70C F. 1 1 1 2 4 + 7 0 C E 2 5 + 1 5 C E 2 5 + 7 0 0 E 1 1 1 2 6 + 7 0 C E 2 7 + 7 0 0 E 2 8 + 7 0 C E 28+77C E 29+52C E 30+70C F 31+24C E 33 + 7CC E 34+70C E 35+70C E 36 + 700 E 37+70C E 3 7 + 7 9 C E 1 1 3 8 + 7 0 C E 1 1 3 9 + 7 0 C E l l 4 0 + 7 0 C E 1 1 4 1 + 7 0 C E l 1 1 1 4 5 + 7 0 C E l 1 1 1 1 1 46+7GC E l 1 1 1 1 1 47+700 E l 1 1 1 1 1 FC5+00 E  FC5+50 E FG6+00 E F10+00 E , . F l l + O O E F12+00 E F13+00 E  CM - < cn 2- < 0 0 _t < OO _t <r oo _S < 0 0 _t <I OO 35 <l UO at <i oo as <c oo 3 1 1 / ) _ <i oo _ <a oo _s <a. oo _s < oo _ < oo _ <t oo 3 t <x oo i n n o LL. i n o LL un o LL LO O o. <t IX ^ LT LL <f cr U- st- cr [ a . sj- co LL -4" CO LL s f CO LL s j - 00 LL St" CO LL -j- >r LL SJ" sj" a . <- sr LL ST NT LL >r sr u . - r - f u- sr <r LL <r < LL sj- sr i x >j- s r LL »r sr LL -T LL s r sr LL s r sr LL T :sT LL s r SI-LL s r sr LL sr sf LL s r sr LL sT LL ro IX. -T ro LL ro LL 4" ro LL ro, t— u r\j t - _ C\J I- O N t ~ _ CM H U M r - O f-> h - U r-l f— t_) —t r - C J -H K U O r - U O h U O p- o o h- o o I— o o r - l_> O h- a o r- oo a r~ u - r r - _ <r r- o <r r - _ O p- o »r P- O r - _ p- co CO r~ O -4 r - o <r p~ <_> <r P- o <P r- _ C P~ o <r P- O -4 r- o r - u -4-r - o <r r - _> ro P- O ro r- o ro r- o ro CM co o CM u <r CM _ s r ' N ; U <r CM a sT w o m CM _ ro CM _> ro CM o ro r~ co o r - O sT r - u s r r - o sr r - <_ sr n r -n -H ro r -fM O o >o ro o o i n p-T O » i n » o o i n o o cc <r •o •o N CC r-vO r -tn r -c. cx r~ r -_ r -m P-c_ cc r- P-~o p~ i n Is-r-4 r -r~ p-v 0 p-i n r~ r H r -o r~ cr i — co p-p- co p- r -ct cx r - r~ _ r-~ i n r— r—' o p-cr r-oo r— p- oo r - P~ CC cc r- Q <; r -i n p~ p-UJ LU LU o o o o o o + + + 4 in co IX. LL IX LU IX! LU —* O O ro c> O + + + co oo cr-•H r - l —4 LL LL LL LU IXi LU O O O q o P-+ + + O rH o CM CM CM IX LL LL LU LU LU 0 O O p~ <r P-+ + + r-^ CM CM 01 ro ro LL LL LU LU UJ O O C CM r - CM + + + CO CM CO CO sT LL LL IX LU LU LU O O CM P~ + + sr sr <r sr LL LL LL U LU IX! o o o f- P- P-•f + + oc cr o <r <r m tx u- i x W Vi W Vi w w w w w w w w w w w w w w w I t A A A A A A A A A A A A A A A A A A A A S S S S S S S S S S S ' S S S S S S S S S T T T T T T T T T T T T T T T T T T T T T O C C C C C C C C C C C C C C C C C C C C T 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 V -< 6 7 8 8 9 0 1 3 4 7 6 7 7 8 9 0 1 5 6 7 0 7 7 7 8 5 7 2 7 7 5 7 7 8 7 7 7 7 7 7 7 A VCLACO N T T T T T T T T T T T T T T T T T T T T 02+OOC E C 03+OOC F C 03+50C E B 04+000 E C 07+00C I C 08+00C E C 08+50C E C 09+00C F B 15+73C £ D 16+00C E 0 16+34C E D 17+00C E 0 22+000 E c 23+70C E D 24+70C E 0 25+15C E D 2 5+70C E D 26+70C E 1 D 27+70C E 1 D 28+70C E 1 D 28+77C E 1 C 29+52C E 1 C 30+70C E 1 c 31+24C E 1 B 33+70C E 1 C 34+70C E 1 D 35+70C E 1 C 36+70C E 1 C 37+700 E 1 C 37+790 E i B 3 8+70C E 1 c 39+70C E 1 B 40+700 E 1 C 41+70C E 1 c 45 + 7CC E 1 C 46+70C E 1 0 47+70C E 1 D F05+00 E c F05+50 k c F06+00 E C F10+00 E B F l l + O O F c F12+00 E D F13+00 E D F13+20 E C F13+67 E D W W W W W W W W W W W W W W Vi w w w w w A A A A A A A A A A A A A A A A A A A A S S S S S S S S S S S S S S S S S S S S T T T T T T T T T T T T T T T T T T T T T O C C C C C C C C C C C C C C C C C C C C T 2 2 2 2 2 3 3 2 3 3 3 3 3 3 3 4 4 4 4 4 V 6 7 8 8 9 0 1 3 4 7 6 7 7 8 9 0 1 6 7 0 1 1 1 5 7 2 7 7 5 7 7 8 7 7 7 7 7 7 7 A -< F 14 + 00 E 0 F 1 5 + 0 0 E G F 1 8 + 0 0 E D F 1 8 + 3 1 E D F 1 8 + 9 0 E D F 19 + 00 E C F 2 0 + 0 0 c ~ D F 2 1 + 0 0 E C F 2 9 + 7 0 E 1 F 3 1 + 7 0 E C F 3 2 + 4 0 c C F 3 2 + 7 0 E c F 3 3 + 2 0 E C F 4 2 + 7 0 E C F 4 3 + 2 0 E C F 4 3 + 7 0 E u F 4 4 + 2 0 E D F 4 4 + 7 0 E B F 4 8 +7 0 E B F 4 9 + 7 0 E D F 5 0 + 7 0 E 0 SYMBOL SUMMARY OF MATRIX RANGE COUNT ( INCL.RHS) Z LESS THAN .000001 Y . 000001 THRU .000009  X . 0 0 0 0 1 0 .000099 W , 0 0 0 1 0 0 . 0 0 0 9 9 9 V . 001000 . 0 0 9 9 9 9  U . 0 1 0 0 0 0 " .099999 T . 1 0 0 0 0 0 : . 9 9 9 9 9 9 350 1 1 . 0 0 0 0 0 0 1.000000 634 A 1.000001 1 0 . 0 0 0 0 0 0 B 1 0 . 0 0 0 0 0 1 1 0 0 . 0 0 0 0 0 0 8 C 1 0 0 . 0 0 0 0 0 1 1 . 0 0 0 . 0 0 0 0 0 0 32 D 1 ,000.000001. 1 0 , 0 0 0 . 0 0 0 0 0 0 26 E 1 0 , 0 0 0 . 0 0 0 0 0 1 1 0 0 , 0 0 0 . 0 0 0 0 0 0 F ICC, OOP. 000001 1 , 0 0 0 , 0 0 0 . 0 0 0 0 0 0  G GREATER THAN 1 , 0 0 0 , 0 0 0 . 0 0 0 0 0 0 P R I M A L O B J = V O L A C O R H S = T O T V O A T I M E = 1 . 2 5 W I N S . P R I C I N G 5 I N V E R T C A L L E D T I M E 1 . 2 6 C U R R E N T I N V E R S E E T A - V E C T O R S 0 E L E M E N T S 0 R E C O R D S . . . . . 1 I T E R A T I O N . . . . . . 0 B A S I S N O . O F R O W S . . . . 6 8 L C G I C A L S 6 8 S T R U C T U R A L S 0 E L E M E N T S . . . . 6 8 I N V E R S E — N U C L E U S 0 T R A N S F O R M E D 0 E T A - V E C T O R S 0 E L E M E N T S ' 0 R E C O R D S 1 T I M E T A K E N 0 . 0 0 P R I M A L O B J = V O L A C O R H S = T O T V O A T I M E = 1 . 2 6 M I N S . P R I C I N G 5 S C A L E = I T E R N U M B E R V E C T O R V E C T O R R E D U C E D S U M N U M B E R I N F E A S O U T I N C O S T I N F E A S M 1 6 6 5 6 2 4 2 2 . C O C O O - 6 8 1 2 8 . 0 M 2 6 5 6 6 3 7 1 2 . 0 0 0 0 0 - 6 8 0 8 4 . 0 M 3 6 4 3 1 3 6 0 2 .00000- 6 7 9 5 3 . 9 4 4 2 9 8 2 . 0 0 0 0 0 - 6 7 8 6 7 . 9 M 5 6 2 6 5 3 6 2 2 . 0 0 0 0 0 - 6 7 8 5 6 . 0 M 6 6 1 2 5 2 5 7 2 . 0 0 0 0 0 - 6 7 7 0 6 . 0 7 4 8 0 2 . 0 0 0 0 0 - 6 7 5 9 4 , 0 M 8 5 9 9 1 6 5 2 . 0 0 0 0 0 - 6 7 4 1 4 . 0 9 3 3 3 1 3 2 . 0 0 0 0 0 - 6 7 2 5 8 . 0 M 1 0 5 7 2 6 2 5 8 2 , 0 0 0 0 0 - 6 7 C 2 2 . 0 1 1 5 7 2 2 . 0 0 0 0 0 - 6 6 8 3 8 . 0 M 1 2 5 5 5 7 2 5 4 2 . 0 0 0 0 0 - 6 6 5 9 7 . 9 M 1 3 5 4 2 2 2 9 0 2 .00000- 6 6 4 5 8 . 0 M 1 4 5 3 6 ' 3 2 . 0 0 0 0 0 - 6 6 1 7 2 . 0 1 5 3 5 3 2 2 2 . 0 0 0 0 0 - £ 5 9 2 6 . 0 M 1 6 5 1 3 7 0 2 . 0 0 0 0 0 - 6 5 5 8 5 . 9 1 7 2 4 2 8 8 2 . 0 0 0 0 0 - 6 5 3 0 2 . 0 1 8 3 9 6 9 2 . 0 0 0 0 0 - 6 5 1 5 8 . 0 M 1 9 4 8 2 1 0 9 2 . 0 0 0 0 0 - 6 4 9 9 0 . 0 M 2 0 4 7 3 2 2 9 6 2 . 0 0 0 0 0 - 6 4 4 2 4 , 0 2 1 4 9 1 6 3 2 . 0 0 0 0 0 - 6 4 C 5 6 . 0 M 2 2 4 5 5 9 2 6 1 2 . 0 0 0 0 0 - 6 3 9 8 8 . 0 M 2 3 4 4 4 3 1 1 1 2 . O O O O C - 6 3 3 7 4 . 0 2 4 3 4 3 2 1 2 , 0 0 0 0 0 - 6 2 8 9 0 . 0 M 2 5 4 2 8 8 8 2 . 0 0 0 0 0 - 6 2 8 8 4 . 0 M 2 & 4 1 5 3 2 0 3 2 . C O O O O - 6 2 1 4 8 . 0 2 7 6 1 3 2 3 2 . 0 0 0 0 0 - 6 1 4 9 0 . 0 M 2 8 3 9 1 4 2 2 4 2 , C O O O O - 6 1 0 2 8 . 0 2 9 3 6 3 3 4 2 . 0 0 0 0 0 - 6 0 6 7 C . 0 K 3 0 3 7 5 5 2 0 6 2 . 0 0 0 0 0 - 6 0 2 6 6 . 0 M 3 1 3 6 2 9 3 0 9 2 . 0 0 0 0 0 - 5 9 3 6 6 . 0 M 3 2 3 5 6 0 3 0 8 2 , 0 0 0 0 0 - 5 9 1 9 6 . 0 M 3 3 3 4 4 1 9 2 2 . 0 0 0 0 0 - 5 8 3 6 6 . 0 M 3 4 _ _ 7 8 3 2 . 0 0 0 0 0 - 5 7 8 7 8 . 0 I N V E R T D E M A N D E D A F T E R 2 3 M A J O R / 3 4 M I N O R I T E R A T I O N S - C L O C K C O N T R O L I N V E R T C A L L E D T I M E 1 . 3 8 C U R R E N T I N V E R S E E T A - V E C T O R S . . . . 3 4 E L E M E N T S ...114 R E C O R D S 1 I T E R A T I O N 3 4 B A S I S N O . O F R O W S . , , . 6 8 L C G I C A L S 3 4 S T R U C T U R A L S . . . . 3 4 E L E M E N T S . . . 1 3 6 I N V E R S E — N U C L E U S . . . . . . . . 0 T R A N S F O R M E D 0 E T A - V E C T O R S . . . . 3 4 E L E M E N T S . . . 1 0 2 R E C O R D S . . . . . 1 T I M E T A K E N 0 . 0 1 PRIMAL TIME = SCALE = OBJ = VOLACG RHS = TOT VGA 1.40 MINS, PRICING I TER NUMBER NUMBER INFEAS VECTOR OUT VECTOR I N REDUCED COST SUM INFEAS M 35 36 37 33 163 109 98 16 7 115 104 2 . 0 0 0 0 0 -2 . 0 0 0 0 0 -2. 0 0 0 0 0 -5 7 5 1 0 . 0 5 7 3 4 8 . 0 5 7 2 6 2 . 0 M 38 M 39 40 32 31 40 46 313 94 14 1 33 1 2 . 0 0 0 0 0 -2 . 0 0 0 0 0 -2. 0000 0-5 7 2 4 6 . C 5 6 0 8 0 . 0 5 5 9 2 4 . 0 M 41 M 42 43 30 30 11 309 28 123 327 315 2 . 0 0 0 0 0 -2 . 0 0 0 0 0 -2 . 0 0 0 0 0 -5 5 1 5 2 . 0 5 4 2 5 2 . 0 53 764 .C M 44 M 4 5 46 28 28 62 203 257 249 170 273 2 . 0 0 0 0 0 -2 . 0 0 0 0 0 -2 . 0 0 0 0 0 -53698 .0 5 3 3 6 6 . 0 5 3 2 1 6 . C 47 M 48 49 28 258 167 261 274 227 29 7 2 . 0 0 0 0 0 -2 . 0 0 0 0 0 -2 . 0 0 0 0 0 -5 3 1 8 8 . 0 53136 .0 5 3 1 3 4 . 0 50 INVERT DEMANDED 242 AFTER 239 8 MAJOR/ 2 . 0 0 0 0 0 -16 MINOR 53 132 .0 ITERATIONS - CLOCK CONTROL t W U C B T r « i 1 C P T T ME OF ROWS . LEUS . . . . 1.45 . . . 68 . . . . 0 M1RRFMT T M \ / P R * : F F T A - \ / F T T H R C ELEMENTS EL EMENTS ELEMENTS . . . 1 9 8 . . . 1 4 6 . . . 1 1 7 RECORDS RECORDS . . . . . 1 ITERATION . BAS IS — INVERS E — NO. — NUC TRANSFORMED 0 ETA-VECTORS . . . . 3 9 . . * . . 1 TIME TAKEN 0.01 PRIKAL OBJ = VOLACO RHS = TOTVOA TIME = SCALE = 1.46 • MINS. PRICING 5 I TER NUMBER M 51 NUMBER INFEAS 28 VECTOR OUT 165 VECTOR I N 139 REDUCED COST 2 . 0 0 0 0 0 -SUM INFEAS 52968.0 M 52 M 53 M 54 2 7 26 25 44 17 58 142 187 278 2.00 0 0 0 -2.OOCOO-2 . 0 0 0 0 0 -5 2 1 3 6 . 0 5 1 0 3 8 . 0 4 9 2 2 6 . 0 M 55 25 INVERT DEMANDED 274 AFTER 351 5 MAJOR/ 2 . 0 0 0 0 0 -5 MINOR 4 9 1 9 6 . 0 ITERATIONS - CLOCK CONTROL i WWFBT r A I i cn TIME OF ROWS . L EUS . . . . 1 .50 . . . 68 • _» » «0 r t l R R F M T T M \ / F R C ; F F T 4 — V F T T O R LL. ELEMENTS ELEMENTS ELEMENTS . . . 1 4 4 . . . 1 5 2 . . . 126 RECORDS RECORDS IT ERAT ION 55 BAS IS - -INVERSE — NO. — NUC TRANSFORMED TIME TAKEN 0 . 0 1 PRIMAL OBJ = VOLACG RHS = TOTVOA TIME = SCALE = 1.51 * MINS. PRICING 5 EXECUTOR. MPS/36G V2-M8 PAGE 8 - 7 0 / 3 3 1 ITER NUMBER VECTCR VECTOR REDUCED SUM NUMBER INFEAS GUT IN COST INFEAS M 56 24 30 310 2 . 0 0 0 0 0 - 49106. 0 M 57 24 296 282 2.00 0 0 0 - 4 8 6 6 0 . 0 J M 5 8 2 4 29 7 355 2 . 0 0 0 0 0 - 4 8 5 6 8 . 0 M 59 24 323 266 2 . 0 0 0 0 0 - 48488 . 0 M 60 23 18 349 2 . 0 0 0 0 0 - 4 7 0 0 4 . 0 M 61 22 64 33 5 2 . 0 0 0 0 0 - 46 630 .0 M 62 21 12 160 2.00000- 4 4 3 1 6 . 0 M 63 2 0 48 116 2.00000- 44288 .0 M 64 20 334 2C7 2.COCOO- 43818 . 0 M 65 20 206 356 2 . 0 0 0 0 0 - 4 3 5 5 2 . C 66 249 261 2.COOOO- 4 3 3 0 4 . 0 M 67 19 37 34 6 2 . 0 0 0 0 0 - 4 2 4 5 2 . 0 M 68 19 356 287 2 . 0 0 0 0 0 - 4 2 1 8 6 . 0 69 261 25 5 2'. 0 0 0 0 0 - 4 1 9 3 8 . 0 M 70 19 282 .334 2 .00 000- 41666. 0 M 71 1 9 254 270 2.00000- 4 1 2 8 8 . 0 72 310 306 2 . 0 0 0 0 0 - 4 1 1 1 8 . 0 73 335 274 2 . 0 0 0 0 0 - 4 1 0 9 4 . 0 M 74 19 290 370 2 . 0 0 0 0 0 - 4 1 0 5 2 . 0 M 75 19 .371 3G4 2.GOCOO- 4 1 0 5 0 . 0 M 76 19 278 345 2 . 0 0 0 0 0 - 4 1 0 2 0 . 0 M 77 19 288 33 2 2 . 0 0 0 0 0 - 4 0 7 6 8 . 0 M 78 18 23 403 1,00 0 0 0 - 4 0 6 2 3 . 0 79 334 336 2 . 0 0 0 0 0 - 40031 .0 M 80 17 63 33 8 2 . 0 0 0 0 0 - 3 9 6 3 7 . 0 M 81 16 38 376 . 2 . 0 0 0 0 0 - 38201 . 0 M 82 16 227 229 2 . 0 0 0 0 0 - 3798 5.0 M 83 15 51. • 185 2, CO000- 3 57 57 .0 M 84 14 15 216 2 . 0 0 0 0 0 - 33659. 0 M 85 13 54 218 2 . 0 0 0 0 0 - 3 1 0 7 7 . 0 M 86 13 321 299 2,COOOO- 3 0 8 4 5 . 0 M 87 13 322 333 2 . 0 0 0 0 0 - 3 0 5 9 9 . 0 INVERT DEMANDED AFTER 27 MAJOR/ 3 2 MINOR ITERATIONS - CLOCK CONTROL INVERT CALLED T IME 1.63 CURRENT INVERSE E TA-VECTORS . . . . 74 ELEMENTS . . . 3 6 1 .2 ITERATION . . BASI S NO.OF ROWS . . . . 6 8 STRUCTURAL S . . . . 54 ELEMENTS . . . 1 7 5 ETA-VECTORS . . . . 54 ELEMENTS . . . 1 6 1 .1 TIME TAKEN 0 .01 PRIMAL OBJ = VOLACO RHS = TOTVOA TIME = 1. 65 MI NS. PRICING 5 : SCALE = * ITER NUMBER VECTOR VECT GR REDUCED SUM NUMBER INFEAS OUT I N COST INFEAS M 88 12 19 177 2. GOOOO- 2 9 8 0 1 . 0 M 89 11 47 15 2 2 . 0 0 0 0 0 - 2 6 9 2 1 . 0 M 90 10 13 134 2.GOOOO- 2 5 7 2 7 . 0 M 91 10 299 3C7 2 . 0 0 0 0 0 - 2 5 2 4 9 . 0 92 116 140 2 . 0 0 0 0 0 - 2 5 2 2 1 . 0 M 93 9 4 5 131 2 . 0 0 0 0 0 - 2 2 2 1 7 . 0 94 306 197 2. 0 0 0 0 0 - 2 2 C 7 9 . 0 ) INVERT DEMANDED AFTER 5 MAJOR/ " 7 MINOR ITERATIONS - CLOCK CONTROL INVERT CALLED TIME 1.68 CURRENT INVERSE ETA-VECTORS ....61 ELEMENTS ...200 RECORDS .....1 ITERATION 94 BASIS NO.OF ROWS ....68 LOGICALS 10 STRUCTURALS ....58 ELEMENTS ...183  INVERSE -- NUCLEUS ........0 TRANSFORMED .....0 ETA-VECTORS .... 58 ELEMENTS ...173 RECORDS 1 TIME TAKEN OToT PRIMAL OBJ = VOLACO RHS = TOTVOA TIME = • 1.70 MINS. PRICING" 5 SCALE = ITER NUMBER VECTOR VECTOR REDUCED SUM NUMBER 1N F E AS OUT IN COST INFEAS M 95 9 229 223 2.00000- 21863.0 M 96 9 134 175 2.00000- 20857.0 97 142 174 2.00000- 20053.0 98 141 173 2. 00 000- 19883.0 M 99 9 222 220 2.COCOO- 19667.0 100 104 100 2.00000- 19 581.0 M 101 8 10 213 2.00000- 19293.0 M 10 2 7 50 178 2. OOCOO- 17971.0 M 103 7 266 275 2.00000- 16743.0 M 104 7 255 259 1.00000- 16430.0 105 308 408 1. 00000- 16267.0 M 106 6 27 407 1 .00000- 16218.0 M 107 6 175 1.92 2.OOCOO- 14996.0 108 174 19 1 2.00 000- 14192.0 109 2 07 206 2.00000- 13456.0 110 213 193 2. 00000- 13168.0 111 173 190 2.00000- 12912.G M 112 5 16 229 2.00000- 12764.0 M 113 5 224 230 2. 00000- 12550.0 1 14 115 117 1.00000- 1246 9.0 M 115 5 220 122 2.00000- 11965.0 116 2 29 196 2.00000- 11817. 0 M 11? 5 216 219 1.00000- 11514.0 118 94 93 1.00000- 11463.0 M 119 4 52 208 1.00000- 11161.0 M 120 3 67 377 1.00000- 9208.00 M 121 2 20 400 i . ooooo- 7011.00 M 122 1 21 401 1. 00000- 4055. OG M 123 0 68 381 1.00000- * FEASIBLE SOLUTION PRIMAL OBJ = VOLACO RHS = TOTVOA TIME = 1.80 MINS. PRICING 5 SCALE = SCALE RESET TO 1.00000  ITER NUMBER VECTOR VECTOR REDUCED FUNCTION NUMBER NONOPT OUT IN COST VALUE M 124 77 170 171 .2.7000- 13783.9 M 125 70 338 348 .15000- 13754.4 ITER NUMBER VECTOR VECTOR REDUCED FUNCTION NUMBER NONOPT OUT IN COST VALUE 126 362 367 . 2 1 0 0 0 - 13753.1 J M 127 58 139 121 . 14 00 0 - 1 3 7 4 0 . 5 \ 128 336 329 . 2 2 0 0 0 - 13 7 2 9 . 3 129 360 31 8 . 1 5 0 0 0 - 13727 .2 130 329 328 . 11000- 13721 .6 M 131 55 206 226 " . 1 2 0 0 0 - 13680.8 132 3 51 31 9 . 1 1 0 0 0 - 1 3 6 4 9 . 7 133 331 320 . 1 1 0 0 0 - 13640. 4 M 134 47 230 179 . 2 0 0 0 0 - 13621 .8 M 135 59 219 217 . 1 5 0 0 0 - 1 3 5 7 6 . 4 136 345 317 . 1 1 0 0 0 - 1 3 5 7 4 . 3 H 137 50 177 399 . 1 3 0 0 0 - 1 3 5 3 0 . 0 138 315 356 . 1 1 0 0 0 - 13503.2 M 139 40 218 215 . 1 2 0 0 0 - . 1 3 2 9 9 . 7 -140 187 186 . 0 1 0 0 0 - 1 3 2 9 8 . 7 M 141 48 178 203 . C 9 0 0 0 - 132 75 .4 142 367 364 . 0 7 0 0 0 - 13270 .4 M 143 36 3 _ 2 34 3 . 0 7 0 0 0 - 13253 .5 144 208 126 . 0 9 0 0 0 - 13243. 7 145 333 344 . 0 7 0 0 0 - 13 2 4 0 . 0 M 146 34 123 173 .07 0 0 0 - 1 3 1 9 3 . 6 M 147 29 122. 149 . C 7 0 0 0 - 1 3 1 7 8 . 7 148 186 180 . 0 3 0 0 0 - 13175 .7 149 407 402 . 0 5 0 0 0 - 13173 .2 M 150 29 270 271 . 0 5 0 0 0 - 13166.2 M 151 26 349 341 . 0 4 0 0 0 - 13158 .0 152 149 214 . C 4 0 0 0 - 13153 .5 M 153 21 217 188 . 0 6 0 0 0 - 13137 .2 M 154 14 .28 7 292 . 0 2 0 0 0 - 1 3 1 2 6 . 6 155 190 195 . 0 6 0 0 0 - 1 3 1 2 3 . 3 M 156 14 192 183 . 0 6 0 0 0 - 13086 .7 157 191 182 . 06 0 0 0 - 13057 .7 M 158 8 18 5 39 8 . 0 4 0 0 0 - 13 0 3 2 . 5 159 188 153 . 0 2 0 0 0 - 1 3 0 1 3 . 4 160 182 151 . 0 2 0 0 0 - 1.3003.7 M 161 7 152 175 . 0 2 0 0 0 - 13003. 7 OPTIMAL SOLUTION SOLUTION ( OPT I MAD TIME = 1.90 MINS. ITERATION NUMBER = . . . N A M E . . . . . . A C T I V I T Y . . . DEFINED AS FUNCTIONAL RESTRAINTS 13003 .73000 VOLACO TOTVOA SECTION 1 - ROWS NUMBER o * * ROW « • AT . . .ACTIVITY.. . SLACK ACTIVITY ..LOWER LIMIT. ..UPPER LIMIT. . DUAL ACTIVITY 1 VOLACO 8S 13003.73000 13003.73000- NONE NONE 1.OOOOO 2 02+OOC EQ 156.000 00 156.00000 156.00000 .03000 3 03+00C EG 170.00000 170.OOOOO 170.OOOOO .03000 4 03+ 50C EQ 56.OCOOO 56 .00000 56.00000 .03000 5 04+00C EQ 135.OOGOO 135.00000 135.00000 .03000 6 07+OOC EC 143 .00000 143.00000 143.00000 .03000 7 c e + o o c EQ 843.OOCGO 843.00000 843 .00000 .03000 8 08+50C EQ 310.00000 310.OOOOG 310.00000 .03000 9 C9+00C EG 90.00000 90.00000 90.00000 .03000 10 15+73C EQ 2909.OOOCO 2909 .00000 2909.00000 .03000 11 16+00C EQ 1204.00000 1204.OOOOC 1204.00000 .03 000 12 16+34C EQ 1654.00000 1654 .00000 1654.00000 .03GOO 13 17+00C EQ 2051.OCCOO 2051.00000 2051.00000 .03000 14 22+OOC EQ 599.00000 599.00000 599.OOOCO .01000-15 23+70C EQ 2163.OOCGO 2163.00000 2163.00000 .11000-16 24+70C EQ 23 88.OCOOO 2388.OOOOC 2388 .00000 .19000-17 25+15C EC 1149.00000 1149.OOOOO 1149.00000 .22000-18 25+70C £ Q 1051.OCOOO 1051 .00000 1051.00000 .26000-19 26+70C EQ 2037.00000 2037,OOOCO 2037.00000 .26000-20 27+70C EQ 2630.00000 2630 .00000 263 0.OOOCO .26000-21 28+70C EQ 2956. OCOOO 2956 .00000 2956 .00000 .26000-22 28+77C EQ 190.00000 190.OOOOC 190.OOOOO .26000-23 29+52C EQ 987.00000 987.00000 987.00000 .26000-24 30+70C EU 142.00000 142,00000 142 .OOOOO .26000-25 31+24C EC 76.00000 76.OOOOO 76.OOOCO .26000-26 33+ 70C EC 118.OCCOO 118 .00000 118.00000 .26000-27 34+70C EQ 1447,OOGOO 1447.00000 1.447 .00000 .26000-28 3 5+70C EQ 857.00000 857 .OOOOC 857.00000 .26000-29 36+70C EQ 484.00000 484,00000 484.00000 .25000-30 37+70C EQ 966.00000 966.OOOOO 966.00000 .18000-31 37+79C EQ 65.00000 65 .00000 65.00000 .18000" 32 3 8+70C EQ 283. OOOCO 283 .00000 283.00000 .11000-33 39+70C EQ 84.00000 84.OOOOG 84.OOOCO .04000-34 4C+70C EQ 242.00000 242.00000 242.00000 .03000 35 41+70C EQ 12 3. 00000 123.00000 123.00000 .03000 36 45+70C EQ 5 08 .00000 508.OOOOO 508.OOOOO . 03000 37 4 6+7 0C E G 1127.OCCOO 1127 .00000 1127.00000 .03000 38 47+70C EQ 1211.OCOOO 1211.00000 1211 .00000 .03000 39 FC5+00 EQ 477 .00000 477.00000 477.OOOCO .29000-40 FC5+50 EQ 616. 00000 616.00000 616 .00000 .29000-41 F06+00 EQ 418.00000 418.00000 418.00000 .29000-42 F1C+00 EQ 43 .00000 43.UU000 43.OOOOO .29000-43 F l l + 0 0 EQ 391.OOOOO 391.00000 391.00000 .29000-44 F12+00 EG 1076.00000 1076.OOOOO 1076.OOOOO .29000-45 F13+00 EQ 2113.OOOOO 2113.00000 2113.00000 .29000-46 F13+20 EQ -• .- 5 8 3. OOOCO 583.00000 583.00000 .29000-47 F.13+67 EQ 1440.00000 1440.OOOOO 1440.OOOCO .29000-48 F 14+00 EQ 1171.OCOOO 1171 .00000 1171.00000 .29000-49 F15-+00 EQ 274.00000 274.OOOOC 274 .00000 .29000--00062* 00000* 550+/ 00000*5 50+/ • 00000 *SSOV 03 01+053 89 -00052* 00000*0162 OOOOO* 0162 * OOOQO *0T62 03 0_+6+/3 L9 -00062* 00000 *22 OOOOO *22 • 00000*22 03 01+8W 99 -00062' 00000*11 OOOOO* ll • OOOOO * U 03 0 _+•*+/=» 59 -00062 * 00000*9621 00000*8621 • 00000*8621 03 02 + +/V3 V9 -00062* 00000' 1911 OOOOO•1911 • 00000*I9_T 03 0_+£t>3 £9 -00092' 00000*+/86 OOOOO* +/86 • OOOOO *+/B- 03 0 2 + £ * 3 29 -00022 • OOOOO *^69 OOOOO * V69 • 00000*^69 03 0Z. + 2V3 19 • 00000* £19 0 0 0 0 0 * £ I 9 • 0 0 0 0 0 * £ 1 9 03 0 2 + £ £ 3 09 V • • 00000*62- 00000*625 * 00000*625 03 0 L+2 £ 3 65 V • 00000 *_66 00000*166 * OOOOO*166 03 0 V + 2 £ 3 85 V • ooooo* c i e 0 0 0 0 0 * £ I £ • OOOOO *£T£ 53 02.+ TE3 IS V * 00000*1 OOOOO*I • OOOOO * I 33 01+623 95 V -0002T* OOOOO *££<? OOOOO *££^ * 00000"££V 03 00+123 55 -00002* 00000*0+/£2 00Q00*0+/£2 • ODOOO *0V£2 03 00+023 VS -000S2 * 00 0 0 0 ' 8 9 £ OOOOO* 89£ • OOOOO *89£ 03 00+6T._ £5 -00012* 00 0 0 0 * 0 8 S £ 0 0 0 0 0 * 0 8 S £ * 00000*Q8S£ 03 06+813 25 ? -00062* 0 0 0 0 0 * £ 9 2 2 OOOOO* £922 • OQOCO *£9 22 03 I£+813 IS -00062* 00000*2692 00000*2692 * 00000*2692 03 00+813 OS A l l A l 1.3 V i v no* •1IWI1 _3ddn* • • l i w n _3MQ1 * * A1.IM13V >T_V1S * * "kL I A H DV IV * *M0_* * * a39WflN V l e e / o i - ex 30Vd 8W- 2A 09E/SdW . *_0ifVJ3X 3 NUMBER .COLUMN. AT ...ACTIVITY INPUT COST.. ..LOWER LIMIT. ..UPPER L I M I T . .REDUCED COST. 69 F050C020 BS 156, ,00000 .26000 NONE 7 0 FC5GCO3 0 BS 43, OOOOO .26000 NONE • A 71 F050C035 LL .26000 NONE • . 72 F050C040 BS 135* .OOOOO .26000 NONE • 73 FG5CCC70 BS 143, .CCCCO .26000 NONE A 74 FO5OC080 LL .26000 NONE • 75 FC5GCC85 LL .30000 NONE .04000 76 F050C090 LL .33000 NONE .07000 A 77 F050BORR LL .29000 NONE 78 FC5 5C02 0 LL .30000 NONE .04000 A 79 F05 5CO3 0 LL .26000 NONE 80 F055C035 BS 56 •OOOOO .26000 NONE A 81 FC55C04C LL .26000 NONE A 82 F055C070 LL .26000 NONE 83 F055C080 BS 560 .00000 .26000 NONE A 84 F 0 5 5C 0 8 5 LL .26000 NONE • 85 F055C090 LL .30000 NONE .04000 A 86 F055B0RR LL .29000 NONE 87 FC6CC020 LL .33000 NONE .07000 88 F060C030 BS 127 .OOOCO .26000 NONE - • A 89 F06CC03 5 LL .26000 NONE • A 90 FC6CC04C LL .2 6000 NONE A 91 F060C070 LL .26000 NONE 92 FG60C 0 80 BS 240, OOOOO .26000 NONE 93 F06 0C08 5 BS 51, , OOOOO .26000 NONE A 94 F060C090 I L .26000 NONE A 95 F C6GB0RR LL .29000 NONE . 96 F100C030 LL .55000 NONE .29000 97 F10OC035 LL .51000 NONE .25000 98 F 100C 040 LL .48000 NONE .22000 A 99 F100C070 LL .26000 NONE 100 F100C080 BS 43 .00000 .26000 NONE A 101 F100C08 5 LL .26000 NONE : A 102 F100C090 LL .26000 NONE 103 F100C157 LL .46000 NONE .20000 104 F100C 160 LL .48000 NONE .22000 105 F100C163 LL .49000 NONE .23000 106 F100C170 LL .55000 NONE .29000 A 107 F100B0RR LL .29000 NONE 108 F110C040 LL .55000 NONE .29000 109 F 11OC 0 7 0 LL .33000 NONE .07000 A 110 F110C080 LL .26000 NUNE • 111 F l I O C 085 BS 259 .00000 .26000 NONE A 112 F l I O C 090 LL .26000 NONE • 113 F110C157 LL .39000 NONE .13000 114 F110C160 LL .40000 NONE .14000 115 F 11 OC 16 3 LL .42000 NONE .16000 11.6 F110C170 LL .48000 NONE .22000 117 F110B0RR BS 132 .00000 .29000 NONE NUMBER .COLUMN. AT . . . AC TI VI TY .'. . ..INPUT COST . . ..LOWER L I M I T . ..UPPER L I M I T . .REDUCED COST. 118 F120C070 LL .40000 NONE .14000 119 F120C080 LL .33000 NONE .07000 J 120 F120C08 5 LL .30000 NONE .04000 \ 121 F120C090 BS 90.00000 .26000 NONE 122 F12CC157 LL .31000 NONE .05000 123 F 120C 160 LL .33000 NONE .07000 124 F120C163 LL .35000 NONE .09000 125 F12 0C170 LL .40000 NONE .14000 126 F12.0B0RR BS 986.C0O00 .29000 NONE • 127 F130C070 LL .48000 NONE .22000 128 F130C080 LL .40000 NONE .14000 129 F130C0 85 LL .37000 NONE .11000 130 F130C090 LL .33000 NONE .07000 131 F130C157 BS 2113.OOOOO .26000 NONE A 132 F130C160 LL .26000 NUNE • 133 F130C163 LL .28000 NONE .02000 134 F13 0C17 0 LL .33000 NONE .07000 A 135 F130B0RR LL .29000 NONE 136 F132C070 LL .49000 NONE .23000 137 F13 2C08 0 LL .42000 NONE .16000 138 F132C085 LL .39000 NONE .13000 139 F132CG90 LL .35000 NONE .09000 140 F132C157 BS 583.OOOOO .26000 NONE A 141 F132C160 LL .26000 NONE 142 F132C 163 LL .28000 NONE .02000 143 F132C170 LL .31000 NONE .05000 A 144 F132B0RR LL .29000 NONE 145 F136C070 LL .53000 NONE .27000 146 F136C080 LL .46000 NONE .20000 147 F136CC85 LL .42000 NONE .16000 148 F136C090 LL .39000 NONE .13000 A 149 F136C157 LL .26000 NONE A 150 F136C160 LI- .26000 NONE 151 F136C163 BS 4E3.CC000 .2 6000 NONE 152 F136C170 LL .28000 NONE ,.02000 153 F136B0RR BS 957.OOOOO .29000 NONE 154 F140C070 LL .55000 NONE .29000 155 F140C080 LL .48000 NONE .22000 156 F140CC85 LL .44000 NONE .18000 157 F140C090 LL .40000 NONE .14000 A 158 F140C157 LL .26000 NONE A 159 F14 0C 16 0 LL .26000 NONE 160 F140C16 3 8S 1171.00000 .26000 NONE A 161 F140C170 I L .26000 NONE A 162 F140B0RR LL .29000 NONE • • 163 F150C080 LL .55000 NONE .29000 164 F150C085 LL .51000 NONE .25000 165 F150C090 LL .48000 NONE .22000 A 166 F150C157 LL .26000 NONE A 167 F 150C 160 LL .26000 NONE A 168 F150C163 LL .26000 NONE N U M B E R • C O L U M N . A T . . . A C T I V I T Y . . . . . I N P U T C O S T . . . . L O W E R L I M I T . . . U P P E R L I M I T . . R E D U C E D C O S T . A 1 6 9 F 1.5 O C 1 7 0 L L . 2 6 0 0 0 N O N E 1 7 0 F 1 5 OC 2 2 0 L L . 5 5 0 0 0 N O N E . 2 5 0 0 0 J 1 7 1 F 1 5 0 B 0 R P B S 2 7 4 . 0 0 0 0 0 . 2 9 0 0 0 N O N E • \ A 1 7 2 F 1 8 OC 1 5 7 L L . 2 6 0 0 0 N O N E 1 7 3 F I . 8 0 C 1 6 0 B S 1 2 C 4 . G O O O O . 2 6 0 0 0 N O N E A 1 7 4 F 1 8 0 C 1 6 3 L L . 2 6 0 0 0 N O N E 1 7 5 F 1 8 0 C 1 7 0 B S 1 . O O O O O . 2 6 0 0 0 N O N E 1 7 6 F 1 8 0 C 2 2 0 L L . 3 3 0 0 0 N O N E . 0 3 0 0 0 1 7 7 F 1 8 0 C 2 3 7 L L . 4 6 0 0 0 N O N E . 0 6 0 0 0 . 1 7 8 F 1 8 0 C 2 4 7 L L . 5 3 0 0 0 N O N E . 0 5 0 0 0 1 7 9 F 1 8 0 B 0 R R B S 1 4 8 7 , 0 0 0 0 0 . 2 9 0 0 0 N O N E 1 8 0 F 1 8 3 C 1 5 7 8 S 2 1 3 . 0 0 0 0 0 . 2 6 0 0 0 N O N E A 1 8 1 F 1 8 3 C 1 6 0 L L . 2 6 0 0 0 N O N E A 1 8 2 F 1 8 3 C 1 6 3 L L . 2 6 0 0 0 N O N E 1 8 3 F 1 8 3 C 1 7 0 B S 2 0 5 0 . 0 0 0 0 0 . 2 6 0 0 0 N O N E 1 8 4 F 1 8 3 C 2 2 0 L L . 3 1 . 0 0 0 N O N E . 0 1 0 0 0 1 8 5 F 1 8 3 C 2 3 7 L L . 4 4 0 0 0 N O N E . 0 4 0 0 0 1 8 6 F 1 8 3 C 2 4 7 L L . 5 1 0 0 0 N O N E . 0 3 0 0 0 1 8 7 F 1 8 3 C 2 5 1 L L . 5 5 0 0 0 N O N E . 0 4 0 0 0 A 1 8 8 F 1 8 3 B 0 R R L L . 2 9 0 0 0 N O N E ' 1 8 9 F 1 8 9 C 1 5 7 L L . 2 8 0 0 0 N O N E . 0 4 0 0 0 1 9 0 F 1 8 9 C 1.60 L L . 2 6 0 0 0 N O N E . 0 2 0 0 0 1 9 1 F 1 8 9 C 1 6 3 L L . 2 6 0 0 0 N O N E . 0 2 0 0 0 1 9 2 F 1 8 9 C 1 7 0 L L . 2 6 0 0 0 N O N E . 0 2 0 0 0 1 9 3 F 1 8 9 C 2 2 0 B S 2 3 1 . O O O O O . 2 8 0 0 0 N O N E 1 9 4 F 1 8 9 C 2 3 7 L L . 3 9 0 0 0 N O N E . 0 1 0 0 0 1 9 5 F 1 8 9 C 2 4 7 B S 1 7 7 8 . O O O O O . 4 6 0 0 0 N O N E • 1 9 6 F 1 8 9 C 2 5 1 B S 1 1 4 9 . 0 0 0 0 0 . 4 9 0 0 0 N O N E 1 9 7 F 1 8 9 C 2 5 7 B S 4 2 2 . 0 0 0 0 0 . 5 3 0 0 0 N O N E 1 9 8 F 1 8 9 B 0 R P . L L . 2 9 0 0 0 N O N E . 0 2 0 0 0 1 9 9 F 1 9 0 C 1 5 7 L L . 2 8 0 0 0 N O N E . 0 6 0 0 0 2 0 0 F 1 9 0 C 1 6 0 L L . 2 6 0 0 0 N O N E . 0 4 0 0 0 2 0 1 F 1 9 0 C 1 6 3 L L . 2 6 0 0 0 N O N E . 0 4 0 0 0 2 0 2 F 1 9 C C 1 7 0 L L • 2 6 0 0 0 N O N E . 0 4 0 0 0 2 0 3 F 1 9 0 C 2 2 0 B S 3 6 8 . O O O O O . 2 6 0 0 0 N O N E 2 0 4 F 1 9 0 C 2 3 7 L L . 3 9 0 0 0 N O N E . 0 3 0 0 0 2 0 5 F 1 9 C C 2 4 7 L L . 4 6 0 0 0 N O N E . 0 2 0 0 0 2 0 6 F 1 9 0 C 2 5 1 L L . 4 9 0 0 0 N O N E . 0 2 0 0 0 2 0 7 F 1 9 0 C 2 5 7 L L . 5 3 0 0 0 N U N E . 0 2 0 0 0 . 2 0 8 F 1 9 O B O R R L L . 2 9 0 0 0 N O N E . 0 4 0 0 0 2 0 9 F 2 0 0 C 1 5 7 L L . 3 5 0 0 0 N O N E . 1 8 0 0 0 2 1 0 F 2 0 0 C 1 6 0 L L . 3 3 0 0 0 N O N E . 1 6 0 0 0 2 1 1 F 2 0 0 C 1 6 3 L L . 3 1 0 0 0 N O N E . 1 4 0 0 0 2 1 2 F 2 0 0 C 1 7 0 L L . 2 6 0 0 0 N O N E . 0 9 0 0 0 2 1 3 F 2 O G C 2 2 0 L L . 2 6 0 0 0 N O N E . 0 5 0 0 0 2 1 4 F 2 0 0 C 2 3 7 B S 2 1 6 3 . O O O O O . 3 1 0 0 0 N O N E 2 1 5 F 2 0 0 C 2 4 7 B S 1 7 7 . 0 0 0 0 0 . 3 9 0 0 0 N O N E A 2 1 6 F 2 0 0 C 2 5 1 L L . 4 2 0 0 0 N O N E A 2 1 7 F 2 0 0 C 2 5 7 L L . 4 6 0 0 0 N O N E 2 1 8 F 2 0 0 C 2 6 7 L L . 5 3 0 0 0 N O N E . 0 7 0 0 0 2 1 9 F 2 0 0 B 0 R R L L . 2 9 0 0 0 N O N E . 0 9 0 0 0 EXECUTOR. MPS/360 V2 -M8 PAGE 17 - 70/331 NUMBER .COLUMN. AT . . .ACTIVITY. . . ..INPUT COST.. ..LOWER LIMIT. . .UPPER L IM I T . .REDUCED COST. 220 F210C157 LL .42000 * NONE .3 3000 221 F21CC160 LL .40000 • NONE .31000 J 222 F210C 163 LL .39000 NONE .30000 223 F210C170 LL .33000 NONE .24000 224 F21 CC220 LL .26000 NONE .13000 225 F210C237 LL .26000 NONE .03000 226 F210C247 BS 433.00000 .31000 NONE 227 F210C 251 LL .35000 NONE .01000 228 F210C 257 LL .39000 NONE .01000 229 F210C267 LL .46000 NONE .08000 2.30 F21 0C277 LL .53000 NONE .15000 231 F210B0RR LL .29000 NONE .17000 232 F297C237 LL .48000 NONE .37000 233 F297C247 LL .40000 NONE .21000 234 F297C251 LL • .37000 NONE .15000 235 F297C257 LL .33000 NONE .07000 A 236 F297C 267 LL .26000 NONE A 237 F297C277 L L .26000 NONE A 238 F297C287 LL .26000 NONE 2 39 F29 7C28 8 BS 1.CCGOO .26000 NONE A 240 F297C295 LL .26000 NONE A 241 F297C307 LL .26000 NONE A 242 F297C312 LL .26000 NONE 243 F297C337 LL .33000 NONE .07000 244 F297C 347 LL .40000 NONE .14000 245 F297C357 LL .48000 NONE .22000 246 F297C367 LL .55000 NUNE .30000 247 F297B0RR LL .29000 NONE .29000 248 F3I7C247 LL .55000 NONE .36000 249 F317C 251 LL .51000 NONE .29000 250 F317C257 LL .48000 NONE .22000 251 F317C267 LL .40000 NONE .14000 252 F317C 277 LL .33000 NONE .07000 A 253 F317C287 LL .26000 NONE A 254 F317C2 8 8 LL .26000 NONE A 25 5 F317C295 LL .26000 NONE A 256 F317C307 LL .26000 NONE A 257 F31 7C312 LL .26000 NONE A 258 F317C 337 LL .26000 NONE 259 F317C347 BS 3 13.00000 .26000 NONE 260 F317C357 LL .33000 NONE .07000 261 F317C 367 LL .40000 NONE .15000 262 F317C377 LL .48000 NONE .30000 263 F 317C 378 LL .48000 NONE .30000 264 F317C387 LL .55000 NONE .44000 265 F317B0RR LL .29000 NONE .29000 266 F324C 257 LL m .53 000 NONE .27000 267 F324C267 LL .46000 NONE .20000 268 F324C277 LL .39000 NONE .13000 269 F324C 287 LL .31000 NONE .05000 270 F32 4C28 8 LL • .31000 * NONE .05000 E X E C U T O R . M P S / 3 6 0 V 2 - M 8 P A G E 1 8 - 7 0 / 3 3 1 N U M B E R . C O L U M N . A T . A C T I V I T Y . . . . . I N P U T C O S T . . . . L O W E R L I M I T . . . U P P E R L I M I T . . R E D U C E D C O S T . 2 7 1 F 3 2 4 C 2 9 5 B S 1 4 0 . O O O O O . 2 6 0 0 0 N O N E A 2 7 2 F 3 2 4 C 3 0 7 L L . 2 6 0 0 0 N O N E / 2 7 3 F 3 2 4 C 3 1 2 B S 7 6 . 0 0 0 0 0 . 2 6 0 0 0 N O N E 2 7 4 F 3 2 4 C 3 3 7 B S 1 1 8 . O O O O O . 2 6 0 0 0 N O N E 2 7 5 F 3 2 4 - C 3 4 7 B S 6 6 3 . 0 0 0 0 0 . 2 6 0 0 0 N O N E 2 7 6 F 3 2 4 C 3 5 7 L L . 2 8 0 0 0 N O N E . 0 2 0 0 0 2 7 7 F 3 2 4 C 3 6 7 L L . 3 5 0 0 0 N O N E . 1 0 0 0 0 2 7 8 F 3 2 4 C 3 7 7 L L . 4 2 0 0 0 N O N E . 2 4 0 0 0 2 7 9 F 3 2 4 C 3 7 8 L L . 4 2 0 0 0 N O N E . 2 4 0 0 0 2 8 0 F 3 2 4 C 3 8 7 L L . 4 9 0 0 0 N O N E . 3 8 0 0 0 2 8 1 F 3 2 4 B 0 R R L L . 2 9 0 0 0 N O N E . 2 9 0 0 0 2 8 2 F 3 2 7 C 2 5 7 L L . 5 5 0 0 0 N O N E . 2 9 0 0 0 2 8 3 F 3 2 7 C 2 6 7 L L . 4 8 0 0 0 N O N E . 2 2 0 0 0 2 8 4 F 3 2 7 C 2 7 7 L L . 4 0 0 0 0 N O N E . 1 4 0 0 0 2 8 5 F 3 2 7 L 2 8 7 L L . 3 3 0 0 0 NUNg . 0 7 0 0 0 2 8 6 F 3 2 7 C 2 8 9 L L . 3 3 0 0 0 N O N E . 0 7 0 0 0 2 8 7 F 3 2 7 C 2 9 5 L L . 2 8 0 0 0 N O N E . 0 2 0 0 0 A 2 8 8 F 3 2 7 C 3 0 7 L L . 2 6 0 0 0 N O N E . • A 2 8 9 F 3 2 7 C 3 1 2 L L . 2 6 0 0 0 N O N E A 2 9 0 F 3 2 7 C 3 3 7 L L . 2 6 0 0 0 N O N E A 2 9 1 F 3 2 7 C 3 4 7 L L . 2 6 0 0 0 N O N E 2 9 2 F 3 2 7 C 3 5 7 BS 5 2 9 . 0 0 0 0 0 . 2 6 0 0 0 N O N E 2 9 3 F 3 2 7 C 3 6 7 L L . 3 3 0 0 0 N O N E . 0 8 0 0 0 2 9 4 F 3 2 7 C 3 7 7 L L . 4 0 0 0 0 N O N E . 2 2 0 0 0 2 9 5 F 3 2 7 C 3 7 8 L L . 4 0 0 0 0 N O N E . 2 2 0 0 0 2 9 6 F 2 2 7 C 3 8 7 L L . 4 8 0 0 0 N O N E . 3 7 0 0 0 2 9 7 F 3 2 7 C 3 9 7 L L . 5 5 0 0 0 N O N E . 5 1 0 0 0 2 9 8 F 3 2 7 B 0 R R L L . 2 9 0 0 0 N O N E . 2 9 0 0 0 2 9 9 F 3 3 2 C 2 6 7 L L . 5 1 0 0 0 N O N E . 2 5 0 0 0 3 0 0 F 3 3 2 C 2 7 7 L L . 4 4 0 0 0 N O N E . 1 8 0 0 0 3 0 1 F 3 3 2 C 2 8 7 L L . 3 7 0 0 0 N O N E . 1 1 0 0 0 3 0 2 F 3 3 2 C 2 8 8 L L . 3 7 0 0 0 N O N E . 1 1 0 0 0 3 0 3 F 3 3 2 C 2 9 5 L L . 3 1 0 0 0 N U N E . 0 5 0 0 0 3 0 4 F 3 3 2 C 3 0 7 B S 1 4 2 . O C O O O . 2 6 0 0 0 N O N E A 3 0 5 F 3 3 2 C 3 1 2 L L . 2 6 0 0 0 N O N E A 3 0 6 F 3 3 2 C 3 3 7 L L . 2 6 0 0 0 N O N E 3 0 7 F 3 3 2 C 3 4 7 B S 4 7 1 . O O O O O . 2 6 0 0 0 N O N E A 3 0 8 F 3 3 2 C 3 5 7 L L . 2 6 0 0 0 N O N E 3 0 9 F 3 3 2 C 3 6 7 L L . 3 0 0 0 0 N O N E . 0 5 0 0 0 3 1 0 F 3 3 2 C 3 7 7 L L . 3 7 0 0 0 N O N E . 1 9 0 0 0 3 1 1 F 3 3 2 C 3 7 8 L L . 3 7 0 0 0 N O N E . 1 9 0 0 0 3 1 2 F 3 3 2 C 3 8 7 L L . 4 4 0 0 0 N O N E . 3 3 0 0 0 3 1 3 F 3 3 2 C 3 9 7 L L . 5 1 0 0 0 N O N E . 4 7 0 0 0 3 1 4 F 3 3 2 B 0 R R L L . 2 9 0 0 0 N O N E . 2 9 0 0 0 3 1 5 F 4 2 7 C 3 5 7 L L . 5 5 0 0 0 N O N E . 0 7 0 0 U 3 1 6 F 4 2 7 C 3 6 7 L L . 4 8 0 0 0 N O N E . 0 1 0 0 0 3 1 7 F 4 2 7 C 3 7 7 B S 4 6 6 . 0 0 0 0 0 . 4 0 0 0 0 N O N E 3 1 8 F 4 2 7 C 3 7 8 B S 6 5 . O O O O O . 4 0 0 0 0 N O N E 3 1 9 F 4 2 7 C 3 8 7 B S 7 9 . O C O O O . 3 3 0 0 0 N O N E 3 2 0 F 4 2 7 C 3 9 7 B S 8 4 . 0 0 0 0 0 . 2 6 0 0 0 N O N E 3 2 1 F 4 2 7 C 4 0 7 L L * . 2 6 0 0 0 N O N E . 0 7 0 0 0 EXECUTOR. MPS/360 V2 -M8 PAGE 19 - 70/331 NUMBER * COLUMN . AT . ..AC TIVITY. . . ..INPUT COST.. ..LOWER LIMIT. ..UPPER LI M I T . .REDUCED COST. 322 F427C417 LL .26000 NONE .07000 32 3 F4 27C4 57 LL .26000 NONE .07000 ) 324 F427C467 LL .33000 NONE .14000 325 F427C477 LL .40000 NONE .21000 326 F427B0RR LI- .29000 NONE .07000 3 27 F432C367 BS 4g4.COOOO .51000 NONE • 328 F432C377 BS 500.00000 .44000 NONE A 229 F432C 378 LL .44000 NONE A 330 F432C387 LL .37000 NONE A 331 F432.C397 LL .30000 NONE 332 F432C407 LL .26000 NONE .03000 333 F432C417 LL .26000 NONE .03000 334 F432C45 7 LL .26000 NONE .03000 335 F4 3 2C467 LL •30000 NONE .07000 336 F43 2C47 7 LL .37000 NONE .14000 337 F432B0RR LL .29000 NONE .03000 338 F437C367 LL .55000 NONE .01000 339 F437C377 LL .48000 NONE .01000 340 F437C378 LL .48000 NONE .01000 341 F437C387 BS 2C4.OOOOO .40000 NONE A 342 F43 7C397 LL .33000 NONE 343 F43 7C407 BS 2 4 2.OCCOO .26000 NONE 344 F437C417 BS 52.00000 .26000 NONE A 345 F43 7C457 LL .26000 NONE 346 F437C467 BS 315.OOOOO .26000 NONE • . 347 F43 7C47 0 LL .33000 NONE .07000 348 F437B0RR BS 948.COQCO .29000 NONE 349 F442C377 LL .51000 NONE .04000 3 50 F442C378 LL .51000 NONE .04000 351 F442C387 LL .44000 NONE .04000 352 F442C397 LL .37000 NONE .04000 353 F442C407 LL . 30000 NONE .04000 A 354 F442C417 LL .26000 NONE 355 F442C457 BS 486.00000 .26000 NONE 356 F44 2C467 BS 812.COOOO .26000 NONE 357 F442C477 LL .30000 NONE .04000 A 358 F442B0RR LL .29000 NONE 359 F44 7C 37 7 LL .55000 NONE .08000 360 F447C378 LL .55000 NONE .08000 361 F447C387 LL .48000 NONE .08000 362 F447C 397 LL .40000 NONE .07000 363 F44 7C407 LL .33000 NONE .07000 364 F447C417 8S 71.00000 .26000 NONE A 365 F447C457 LL .26000 NONE • A 366 F447C467 LL .26000 NONE . A 367 F447C477 LL .26000 NONE A 368 F447B0RR LL .29000 NONE 369 F487C417 LL .55000 NONE .29000 370 F487C457 BS 22.OOOOO .26000 NONE A 371 F487C467 LL .26000 NONE A 372 F487C477 LL .26000 NONE NUMBER .COLUMN. AT . ..ACTIVITY. . . ..INPUT COST.. . . LOW ER L I M I T . ..UPPER LIMIT. .REDUCED COST. A 373 F487B0RR LL .29000 NONE # 374 F497C457 LL .33000 NONE .07000 J A 375 F497C467 1 L .26000 NONt 376 F49 7C477 BS 1211.coodo .26000 NONE 377 F497B0RR BS 1699 .00000 .29000 NONE 37 8 F507C457 LL .40000 NONE .14000 379 F507C467 LL .33000 NONE .07000 A 380 F50 7C47 7 LL .26000 NONE 381 F507BORR BS 4055.OOOOO .29000 NONE 382 WASTC020 LL .26000 NONE .29000 383 WASTC030 LL .26000 NONE .29000 384 WASTC035 LL .26000 NONE .29000 385 WASTC040 LL • .26000 NONE .29000 3 86 WASTC 07 0 LL .26000 NONE .29000 387 WASTC080 LL .2 6000 NONE .29000 388 WASTC08 5 LL .26000 NONE .29000 389 WASTC090 LL .26000 NONE .29000 390 WASTC157 LL .26000 NONE .29000 391 WASTC160 LL .26000 NONE .29000 392 WASTC163 LL .26000 NONE .29000 393 WASTC170 LL .26000 NONE .29000 394 WASTC220 LL .26000 NONE .25000 395 WASTC237 LL .26000 NONE .15000 396 WASTC247 LL .26000 NONE .07000 397 WASTC251 LL .26000 NONE .04000 398 WASTC 257 BS 629. COOOO .26000 NONE 399 WAS TC267 BS 2037.00000 .26000 NONt • 400 WASTC 277 BS 2630.00000 .26000 NONE 401 WASTC287 BS 2956.COOOO .26000 NONE 402 WASTC288 BS 189 .00000 .26000 NONE 403 WASTC295 BS 847.COOOO .26000 NONE A 404 WASTC307 LL .26000 NONE A 405 WASTC31. 2 LL .26000 NONE A 406 WASTC 337 LL .26000 NONE A 407 WASTC347 LL .26000 NONE # 408 WASTC375 BS 328.00000 .26000 NONE 409 WASTC 367 LL .26000 _ NONE .01000 410 WAS TC377 LL .26000 NONE .08000 411 WASTC 378 I L .26000 NONE .08000 412 WASTC387 LL .26000 NONE .15000 413 WASTC397 LL .26000 NONE .22000 414 WASTC407 LL .26000 NONE .29000 415 WAST C417 LL .26000 NONE .29000 416 WASTC457 LL .26000 NONE .29000 417 WASTC467 LL .26000 NONE .29000 418 WASTC477 LL • .26000 • NONE .29000 EXECUTOR. EXIT - TI HE = 2.45 IEF373I IEF374I IEF375I IEF376 I STEP STEP JOB JOB / G / G /OPTVOL /OPTVOL START STOP START STOP NUMBER OF I/O INTERRUPTS: 7 033 1. C2 25 70331.0228 70331.0224 70331.0228 10283 CPU 01MIN 16.00SEC MAIN 8CK LCS CPU 01MIN 32.00SEC OK NUMBER LOCKED O U T : ; I T NUMBER IN NON-VIRTUAL STATE: 9626 NUMBER OF SVC INTERRUPTS: 19081 EXECUTION TERMINATED $SIGNOFF ulatea v o l u m e - C • IX -3 Pi ~0> /i J-JJ 3 _L4 t-yj—H--i i t j t i _ . l — | — _ _!_I_L 1 - 1 -JXX _ _ — ft "8 4 - 4 . 4 -' t - J I I i hSJ I - -| - . . - f -U r i L IS I -U -O-4-<- \ n r - - r - - — 1 ::.:lt o..; i rr r i — m 44-1-+--4-ft m - — jg* . U — 5 - 4-P Q r r j f - i - r <<v As -U-U _ J _ U , ttrxtt tt t l r \ < U l - 4 - -4-T T r r t f H 4 T i -x r irr t . J : _ 1 U < 1 1 i ( i l l 4-4-tt 4 _ h - r l -_ _ X [ I 1 J._l..i_L "ht" J-4--4-_ J — i u waste! t,ioocw«|-i . L . J —i \ \ ~ — 1 _ 8" c 1 _L_L O-T T " ^ 5 — — I 'A ft \ \,3aO x t t -1 - -4 n—--|— p. -i—L 4 - t -4 - 4 -T T "Cr m—rCr - T-"ax -c i * l i d 4 - 4 -H-" " t t 

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