# Consider the following linear program: Min8X + 12Y s.t. 1X + 3Y 9 2X + 2Y 10 6X + 2Y 18 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

Chapter 8, Problems #3

Consider the following linear program:

Min8X + 12Y

s.t.

1X + 3Y â‰¥ 9

2X + 2Y â‰¥ 10

6X + 2Y â‰¥ 18

X, Y â‰¥ 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 optimal solution.

c. 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.

d. The Management Scientist computer solution for the linear program in part (a) provides the following objective coefficient range information: How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving theproblem?

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