1. Consider the following linear program: Max 3a + 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 func tion 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 objec tive coefficient range information: Objective Allowable Allowable Variable Coefficient increase 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?

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?