Consider the following linear program.

Max 3A + 2B

s.t. 1A + 1B 10

3A + 1B 26

1A + 2B 18

A, B 0

(a) Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal solution? ____ at (A, B) = ____

(b) Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point _____ (remains, becomes) optimal. The value of the objective function becomes ____.

(c) Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point ____ optimal. The value of the objective function becomes _____ .

(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). The objective coefficient range for variable A is ____ to____ . Since the change in part (b) is (within, outside) this range, we know the optimal solution (will, will not) change. The objective coefficient range for variable B is ____ to ____. Since the change in part (c) is (within, outside) this range, we know the optimal solution (will,will not) change.