Problem 1

Consider the following linear program:

Max 3A + 2B

s.t.

1A + 1B ≤ 10

3A + 1B ≤ 24

1A + 2B ≤ 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 optimal solution.

d. The computer solution for the linear program in part (a) provides the following objective coefficient range information:

Variable Objective Coefficient Allowable Increase Allowable Decrease

A........................3.00000........................3.00000..................1.00000

B........................2.00000.........................1.00000.................1.00000

Use this objective coefficient range information to answer parts (b) and (c).

2    Consider below the linear programming problem: Max 3A+2B s.t. 1A+1B≤10 3A+1B≤24 1A+2B≤16 A,B≥0 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 shadow price for constraint 1. 

c. The sensitivity analysis for the linear program in this problem provides the following right-hand side range information: 

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