Consider below the linear programming problem:

Max 3A+2B

s.t.

1A+1B10

3A+1B24

1A+2B16

A,B0

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 analysis for the linear program in this problem provides the following right-hand side range information:

Constraint Constraint R.H. side Allowable increase Allowable decrease

1 10 1.20 2

2 24 6 6

3 16 Infinite 3

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

d. The shadow price for constraint 2 is 0.5. Using this shadow price and the right-hand-side range information in part (c), what conclusion can you draw about the effect of changes to the right-hand side of constraint 2?