1. Consider the following linear program: Max 3A + 2B s.t. 1A 1B 3A 1B 1A + 2B 10 24 16 A, B ≥ 0 a. Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficient for A changes from 3 to 5. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. c. Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Does the optimal

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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1. Consider the following linear program:
Max 3A + 2B
s.t.
1A
1B
3A
1B
1A + 2B
10
24
16
A, B≥ 0
a. Use the graphical solution procedure to find the optimal solution.
b. Assume that the objective function coefficient for A changes from 3 to 5. Does
the optimal solution change? Use the graphical solution procedure to find the
new optimal solution.
c. Assume that the objective function coefficient for A remains 3, but the
objective function coefficient for B changes from 2 to 4. Does the optimal
Transcribed Image Text:1. Consider the following linear program: Max 3A + 2B s.t. 1A 1B 3A 1B 1A + 2B 10 24 16 A, B≥ 0 a. Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficient for A changes from 3 to 5. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. c. Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Does the optimal
solution change? Use the graphical solution procedure to find the new
solution.
optimal
2. Consider the linear program in Problem 1. The value of the optimal solution is 27. Suppose
that the right-hand side for constraint 1 is increased from 10 to 11.
a. Use the graphical solution procedure to find the new optimal solution.
b. Use the solution to part (a) to determine the dual value for constraint 1.
Transcribed Image Text:solution change? Use the graphical solution procedure to find the new solution. optimal 2. Consider the linear program in Problem 1. The value of the optimal solution is 27. Suppose that the right-hand side for constraint 1 is increased from 10 to 11. a. Use the graphical solution procedure to find the new optimal solution. b. Use the solution to part (a) to determine the dual value for constraint 1.
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