3. Consider the following linear program:

Min 8X 12Y s.t.

1X 3Y 9 2X 2Y10 6X 2Y18

X, Y 0

a. Use the graphical solution procedure to find the optimal solution.

b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new opti-

mal solution.

c. Assume that the objective function coefficient for X remains 8, but the objective func-

tion coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the

graphical solution procedure to find the new optimal solution.

d. The sensitivity report for the linear program in part (a) provides the following objec-

tive coefficient range information:

How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the problem?