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21. Consider the following linear program: Маx 2A + 3В s.t. 5A + 5B < 400 Constraint 1 - 1A + 1B < 10 Constraint 2 1A + 3B > 90 Constraint 3 А, В 2 0 Figure 2.22 shows a graph of the constraint lines. a. Place a number (1, 2, or 3) next to each constraint line to identify which constraint it represents. b. Shade in the feasible region on the graph. c. Identify the optimal extreme point. What is the optimal solution? d. Which constraints are binding? Explain. e. How much slack or surplus is associated with the nonbinding constraint? FIGURE 2.22 GRAPH OF THE CONSTRAINT LINES FOR EXERCISE 21 В 90 80 70 60 50 - 40 30 10 10 20 30 40 50 60 70 80 90 A 100 20

21. Consider the following linear program: Маx 2A + 3В s.t. 5A + 5B < 400 Constraint 1 - 1A + 1B < 10 Constraint 2 1A + 3B > 90 Constraint 3 А, В 2 0 Figure 2.22 shows a graph of the constraint lines. a. Place a number (1, 2, or 3) next to each constraint line to identify which constraint it represents. b. Shade in the feasible region on the graph. c. Identify the optimal extreme point. What is the optimal solution? d. Which constraints are binding? Explain. e. How much slack or surplus is associated with the nonbinding constraint? FIGURE 2.22 GRAPH OF THE CONSTRAINT LINES FOR EXERCISE 21 В 90 80 70 60 50 - 40 30 10 10 20 30 40 50 60 70 80 90 A 100 20

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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21. Consider the following linear program: Мax 2A + ЗВ s.t. 5A + 5B < 400 Constraint 1 - 1A + 1B < 10 Constraint 2 1A + 3B > 90 Constraint 3 А, В > 0 Figure 2.22 shows a graph of the constraint lines. a. Place a number (1, 2, or 3) next to each constraint line to identify which constraint it represents. b. Shade in the feasible region on the graph. c. Identify the optimal extreme point. What is the optimal solution? d. Which constraints are binding? Explain. How much slack or surplus is associated with the nonbinding constraint? е. FIGURE 2.22 GRAPH OF THE CONSTRAINT LINES FOR EXERCISE 21 B 90 80 70 60 50 - 40 30 20 10 10 30 40 50 60 70 80 90 A 100 20
Transcribed Image Text:21. Consider the following linear program: Мax 2A + ЗВ s.t. 5A + 5B < 400 Constraint 1 - 1A + 1B < 10 Constraint 2 1A + 3B > 90 Constraint 3 А, В > 0 Figure 2.22 shows a graph of the constraint lines. a. Place a number (1, 2, or 3) next to each constraint line to identify which constraint it represents. b. Shade in the feasible region on the graph. c. Identify the optimal extreme point. What is the optimal solution? d. Which constraints are binding? Explain. How much slack or surplus is associated with the nonbinding constraint? е. FIGURE 2.22 GRAPH OF THE CONSTRAINT LINES FOR EXERCISE 21 B 90 80 70 60 50 - 40 30 20 10 10 30 40 50 60 70 80 90 A 100 20
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