Consider the following linear program. Min 8X + 12Y

s.t.

1X + 3Y 8

2X + 2Y 12

6X + 2Y 16

X, Y 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 (X, Y) =

(b) Assume that the objective function coefficient for X changes from 8 to 6. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point (X, Y) = remains optimal. The value of the objective function becomes .

(c) Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point (X, Y) = becomes 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 X 8.00000 4.00000 4.00000 Y 12.00000 12.00000 4.00000 How would this objective coefficient range information help you answer parts (b) and (c) prior to re-solving the problem? The objective coefficient range for variable X is to . Since the change in part (b) is within this range, we know the optimal solution will not change. The objective coefficient range for variable Y is to . Since the change in part (c) is outside this range, we know the optimal solution will