C02 LP 12ed

# C02 LP 12ed - PROBLEMS 1 Which of the following...

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PROBLEMS 1. Which of the following mathematical relationships could be found in a linear programming model, and which could not? For the relationships that are unacceptable for linear pro- grams, state why. vr-ys . -- a. -lA + 2B 5 70 b. 2A - 2B = 50 9 I-> c. 1A - 2~* 5 10 d. 3~+2~215 e. lA+ 1B=6 ShZiW. f. + 5B + 1AB 5 25 2. Find the solutions that satisfy the following constraints: a 4A+2B516 4A + 2BZ 16 4A +2B= 16 3. Show a separate graph of the constraint lines and the solutions that satisfy each of the fol- lowing constraints: 3A + 2BS 18 b. 12A + 8B 1 480 e. 5A + 10B = 200

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test - Chapter 2 An Introduction to Linear Programming 4. Show a separate graph of the constraint lines and the solutions that satisfy each of the fol- lowing constraints: I a. 3A - 4B 160 b. -6A + 5B 560 c. 5A - 2B 5 0 5. A 1 0.25 (A + B) b. B50.10(A + c. A 5 0.50 (A + 6. Three objective functions for linear programming problems are 7A + 10B, 6A + 4B, and EL -4A + 7B. Show the graph of each for objective function values equal to 420. 7. Identify the feasible region for the following set of constraints: A,B10 Identify the feasible region for the following set of constraints: 10. For the linear program SELF tes Max 2A+3B s.t. 1A + 2B 5 6 + 3B 5 15 A,B1O find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution? Solve the following linear program using the graphical solution procedure. + 5B s.t. 1A 5 100 1B 5 80 2A + 4B I 400 A,BZ0
Problems 12. Consider the following linear programming problem: Max 3A + 3B s.t. 2A+4BS 12 6A + 4B 5 24 A,B?O a. Find the optimal solution using the graphical solution procedure. b. If the objective function is changed to 2A + 6B, what will the optimal solution be? c. How many extreme points are there? What are the values of A and B at each extreme point? SELI 13. Consider the following linear program: 1A + 2B 5 5 1B 5 4 2A+2B= 12 A,B2O a Show the feasible region. What the extreme points of the feasible region? Find the optimal solution using the graphical procedure. 14. RMC, Inc., is a small firm that produces a variety of chemical products. In a particularpro- duction process, three raw materials blended (mixed together) to produce two prod- ucts: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of % ton of material 1 and 9/a of material 3. A ton of solvent base is a mixture of '/a ton of material 1, 1/6 2, and YiO ton of material 3. After deducting relevant costs, the profit con- tribution is \$40 for every ton of fuel additive produced and \$30 for every ton of solvent base produced. RMC's production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Raw Material Amount Available for Production Material 1 20 tons Material 2 5 tons .. . Material 3 21 Assuming that RMC is interested in maximizing the total profit contribution, answer the following: a What is the linear programming model for this problem? Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced, and what is the projected total profit contribution?

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C02 LP 12ed - PROBLEMS 1 Which of the following...

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