Chapter 3 - Linear Programming: Sensitivity Analysis and Interpretation of Solution

Question 6. Consider the following linear program:

Min 8X + 12Y

s.t.

1X + 3Y 9

2X + 2Y 10

6X + 2Y 18

X, Y 0

a. Use the MS Excel Solver to find the optimal solution with sensitivity analysis and provide the reports by copying or taking screenshot from excel. After providing report calculate the optimal solution.

b. Based on the computer solution (sensitivity analysis report) for the linear program in part (a):

Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change?

c. Based on the computer solution (sensitivity analysis report) for the linear program in part (a):

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?

d. Based on the computer solution (sensitivity analysis report) for the linear program in part (a):

Determine the dual value for constraint 1.

e. Based on the computer solution (sensitivity analysis report) for the linear program in part (a):

Suppose that the right-hand side for constraint 1 is increased from 9 to 10. Find the new optimal solution. What does the right-hand-side range information for constraint 1 tell you about the dual value for constraint 1?

f. The dual value for constraint 2 is 3. Using this dual value and the right-hand-side range information in part (a), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2?