1) Consider the following linear program:

Max3A + 2B

S.t.

1A + 1B < 10

3A + 1B < 24

1A + 2B < 16

A, B > 0

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

b. Assume that the objective function coefficient for a changes from 3 to 5. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.

c. Assume that the objective function coefficient for a remains 3, but the objective function coefficient for B changes from 2 to 4. 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 objective coefficient range information:

Variable Object Coefficient Allowable Increase Allowable Decrease

A 3.000 3.000 1.000

B 2.000 1.000 1.000

Use this objective coefficient range information to answer parts (b) and (c).

2) Consider the linear program in Problem 1. The value of the optimal solution is 27. Suppose that the right-hand side for constraint 1 is increased from 10 to 11.

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

b)Use the solution to part (a) to determine the shadow price for constraint 1.

c)The sensitivity report for the linear program in Problem 1 provides the following right- hand-side range information

Constraint Constraint R.H.Side Allowable Increase Allowable Decrease

1 10.000 1.200 2.000

2 24.000 6.000 6.000

3 16.000 Infinite 3.000

What does the right-hand-side range information for constraint 1 tell you about the shadow price for constraint 1?

Instructions:

These problems focus on finding solutions to numerical problems. With that in mind, most problem sets will include a number of problems. For each problem, it will need to provide more than a simple numerical response. The solutions should thoroughly address the issue and present your findings in a meaningful format, similar to those developed within the chapters and as part of the review exercises solutions. Any Excel spreadsheet or software models developed to solve the problems should be included.