Solution Manual Spreadsheet Modeling And Decision Analysis A Practical Introduction To Business Analytics 8th Edition

SOLUTION MANUAL SPREADSHEET MODELING AND DECISION ANALYSIS A PRACTICAL INTRODUCTION TO BUSINESS ANALYTICS 8TH EDITION s-analytics-8th-edition-ragsdale-solutions-manual/ Chapter 2 - Introduction to Optimization & Linear Programming : S-1 ———————————————————————————————————————————— Chapter 2 Introduction to Optimization & Linear Programming 1. If an LP model has more than one optimal solution it has an infinite number of alternate optimal solutions. In Figure 2.8, the two extreme points at (122, 78) and (174, 0) are alternate optimal solutions, but there are an infinite number of alternate optimal solutions along the edge connecting these extreme points. This is true of all LP models with alternate optimal solutions. 2. There is no guarantee that the optimal solution to an LP problem will occur at an integer-valued extreme point of the feasible region. (An exception to this general rule is discussed in Chapter 5 on networks). 3. We can graph an inequality as if they were an equality because the condition imposed by the equality corresponds to the boundary line (or most extreme case) of the inequality. 4. The objectives are equivalent. For any values of X and X 1 2 , the absolute value of the objectives are the same. Thus, maximizing the value of the first objective is equivalent to minimizing the value of the second objective. 5. a. linear b. nonlinear c. linear, can be re-written as: 4 X - .3333 X 1 2 = 75 d. linear, can be re-written as: 2.1 X + 1.1 X - 3.9 X 1 2 3 ≤ 0 e. nonlinear 6. Chapter 2 - Introduction to Optimization & Linear Programming : S-2 ———————————————————————————————————————————— 7. 8. X2 20 (0, 15) obj = 300 15 (0, 12) obj = 240 10 (6.67, 5.33) obj =140 5 (11.67, 3.33) obj = 125 (optimal solution) X1 0 5 10 15 20 25 Chapter 2 - Introduction to Optimization & Linear Programming : S-3 ———————————————————————————————————————————— 9. 10. Chapter 2 - Introduction to Optimization & Linear Programming : S-4 ———————————————————————————————————————————— 11. 12. Chapter 2 - Introduction to Optimization & Linear Programming : S-5 ———————————————————————————————————————————— 13. X = number of softballs to produce, X = number of baseballs to produce 1 2 MAX 6 X + 4.5 X 1 2 ST 5X + 4 X 1 2 ≤ 6000 6 X + 3 X 1 2 ≤ 5400 4 X + 2 X 1 2 ≤ 4000 2.5 X + 2 X 1 2 ≤ 3500 1 X + 1 X 1 2 ≤ 1500 X , X 1 2 ≥ 0 14. X = number of His chairs to produce, X = number of Hers chairs to produce 1 2 MAX 10 X + 12 X 1 2 ST 4 X + 8 X 1 2 ≤ 1200 8 X + 4 X 1 2 ≤ 1056 2 X + 2 X 1 2 ≤ 400 4 X + 4 X 1 2 ≤ 900 1 X - 0.5 X 1 2 ≥ 0 X , X 1 2 ≥ 0 Chapter 2 - Introduction to Optimization & Linear Programming : S-6 ———————————————————————————————————————————— 15. X = number of propane grills to produce, X = number of electric grills to produce 1 2 MAX 100 X + 80 X 1 2 ST 2 X + 1 X 1 2 ≤ 2400 4 X + 5 X 1 2 ≤ 6000 2 X + 3 X 1 2 ≤ 3300 1 X + 1 X 1 2 ≤ 1500 X , X 1 2 ≥ 0 Chapter 2 - Introduction to Optimization & Linear Programming : S-7 ———————————————————————————————————————————— 16. X = number of generators, X = number of alternators 1 2 MAX 250 X + 150 X 1 2 ST 2 X + 3 X 1 2 ≤ 260 1 X + 2 X 1 2 ≤ 140 X , X 1 2 ≥ 0 17. X = number of generators, X = number of alternators 1 2 MAX 250 X + 150 X 1 2 ST 2 X + 3 X 1 2 ≤ 260 1 X + 2 X 1 2 ≤ 140 X 1 ≥ 20 X 2 ≥ 20 d. No, the feasible region would not increase so the solution would not change -- you'd just have extra (unused) wiring capacity. Chapter 2 - Introduction to Optimization & Linear Programming : S-8 ———————————————————————————————————————————— 18. X = proportion of beef in the mix, X = proportion of pork in the mix 1 2 MIN .85 X + .65 X 1 2 ST 1X + 1 X = 1 1 2 0.2 X + 0.3 X 1 2 ≤ 0.25 X , X 1 2 ≥ 0 19. T= number of TV ads to run, M = number of magazine ads to run MIN 500 T + 750 P ST 3T + 1P ≥ 14 -1T + 4P ≥ 4 0T + 2P ≥ 3 T, P ≥ 0 Chapter 2 - Introduction to Optimization & Linear Programming : S-9 ———————————————————————————————————————————— 20. X = # of TV spots, X = # of magazine ads 1 2 MAX 15 X + 25 X 1 2 (profit) ST 5 X + 2 X < 100 (ad budget) 1 2 5 X + 0 X 1 2 ≤ 70 (TV limit) 0 X + 2 X 1 2 ≤ 50 (magazine limit) X , X 1 2 ≥ 0 X2 40 (0,25) (10,25) 30 15X1+25X2=775 20 (14,15) 10 15X1+25X2=400 (14,0) 20 10 X1 21. X = tons of ore purchased from mine 1, X = tons of ore purchased from mine 2 1 2 MIN 90 X + 120 X (cost) 1 2 ST 0.2 X + 0.3 X > 8 (copper) 1 2 0.2 X + 0.25 X > 6 (zinc) 1 2 0.15 X + 0.1 X > 5 (magnesium) 1 2 X , X 1 2 ≥ 0 Chapter 2 - Introduction to Optimization & Linear Programming : S-10 ———————————————————————————————————————————— 22. R = number of Razors produced, Z = number of Zoomers produced MAX 70 R + 40 Z ST R + Z ≤ 700 R – Z ≤ 300 2 R + 1 Z ≤ 900 3 R + 4 Z ≤ 2400 R, Z ≥ 0 23. P = number of Presidential desks produced, S = number of Senator desks produced MAX 103.75 P + 97.85 S ST 30 P + 24 S ≤ 15,000 1 P + 1 S ≤ 600 5 P + 3 S ≤ 3000 P, S ≥ 0 Chapter 2 - Introduction to Optimization & Linear Programming : S-11 ———————————————————————————————————————————— 24. X = acres planted in watermelons, X = acres planted in cantaloupes 1 2 MAX 256 X + 284.5 X 1 2 ST 50 X + 75 X 1 2 ≤ 6000 X + X 1 2 ≤ 100 X , X 1 2 ≥ 0 X2 (0, 80) obj = 22760 100 75 (60, 40) obj =26740 (optimal solution) 50 25 (100, 0) obj = 25600 0 X1 0 25 50 75 100 125 25. D = number of doors produced, W = number of windows produced MAX 500 D + 400 W ST 1 D + 0.5 W ≤ 40 0.5 D + 0.75 W ≤ 40 0.5 D + 1 W ≤ 60 D, W ≥ 0 Chapter 2 - Introduction to Optimization & Linear Programming : S-12 ———————————————————————————————————————————— 26. X = number of desktop computers, X = number of laptop computers 1 2 MAX 600 X + 900 X 1 2 ST 2 X + 3 X 1 2 ≤ 300 X 1 ≤ 80 X 2 ≤ 75 X , X 1 2 ≥ 0 Case 2-1: For The Lines They Are A-Changin’ 1. 200 pumps, 1566 labor hours, 2712 feet of tubing. 2. Pumps are a binding constraint and should be increased to 207, if possible. This would increase profits by $1,400 to $67,500. 3. Labor is a binding constraint and should be increased to 1800, if possible. This would increase profits by $3,900 to $70,000. 4. Tubing is a non-binding constraint. They’ve already got more than they can use and don’t need any more. 5. 9 to 8: profit increases by $3,050 8 to 7: profit increases by $850 7 to 6: profit increases by $0 6. 6 to 5: profit increases by $975 5 to 4: profit increases by $585 4 to 3: profit increases by $390 7. 12 to 13: profit changes by $0 13 to 14: profit decreases by $760 14 to 15: profit decreases by $1,440 Chapter 2 - Introduction to Optimization & Linear Programming : S-13 ———————————————————————————————————————————— 8. 16 to 17: profit changes by $0 17 to 18: profit changes by $0 18 to 19: profit decreases by $400 9. The profit on Aqua-Spas can vary between $300 and $450 without changing the optimal solution. 10. The profit on Hydro-Luxes can vary between $233.33 and $350 without changing the optimal solution. Spreadsheet Modeling & Decision Analysis A Practical Introduction to Business Analytics th 8 edition Cliff T. Ragsdale Chapter 2 Introduction to Optimization and Linear Programming Introduction  We all face decision about how to use limited resources such as: – Oil in the earth – Land for dumps – Time – Money – Workers Mathematical Programming...  MP is a field of management science that finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual of a business.  a.k.a. Optimization Applications of Optimization  Determining Product Mix  Manufacturing  Routing and Logistics  Financial Planning Characteristics of Optimization Problems  Decisions  Constraints  Objectives General Form of an Optimization Problem MAX (or MIN): f0 (X1 , X2 , …, Xn ) Subject to: f1 (X1 , X2 , …, Xn )=bk : fm (X1 , X2 , …, Xn )=bm Note: If all the functions in an optimization are linear, the problem is a Linear Programming (LP) problem Linear Programming (LP) Problems MAX (or MIN): c1 X1 + c2 X2 + … + cn Xn Subject to: a11 X1 + a12 X2 + … + a1n Xn =bk : am1 X1 + am2 X2 + … + amn Xn = bm An Example LP Problem Blue Ridge Hot Tubs produces two types of hot tubs: Aqua-Spas & Hydro-Luxes. Aqua-Spa Hydro-Lux Pumps 1 1 Labor 9 hours 6 hours Tubing 12 feet 16 feet Unit Profit $350 $300 There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available. 5 Steps In Formulating LP Models: 1. Understand the problem. 2. Identify the decision variables. X1 =number of Aqua-Spas to produce X2 =number of Hydro-Luxes to produce 3. State the objective function as a linear combination of the decision variables. MAX: 350X1 + 300X2 5 Steps In Formulating LP Models (continued) 4. State the constraints as linear combinations of the decision variables. 1X1 + 1X2