Consider the following linear program:

Min 8X + 12Y

S.t.

1X + 3Y 9

2X + 2Y 2 10

6X + 2Y 18

X, 1 20

1. Use the graphical solution procedure to find the optimal solution.
2. 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 optimal solution.
3. Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.
4. The sensitivity report for the linear program in part (a) provides the following objective coefficient range information

Variable	Objective Coefficient	Allowable Increase	Allowable Decrease
	8.000	4.000	4.000
Y	12.000	12.000	4.000

How would this objective coefficient range information help you answer parts (b) and

(c) prior to resolving the problem?