# How much could the profit on X increase or decrease without changing the values of X and Y in the optimal solution?

Answer following questions

· 7.31

· 7.32

· 7.33

1. 7-31 Consider the following LP problem:

Maximize profit=5X+6Ysubject to2X+Y≤1202X+3Y≤240X,Y≥0Maximize profit=5X+6Ysubject to2X+Y≤1202X+3Y≤240X,Y≥0

a. What is the optimal solution to this problem? Solve it graphically.

b. If a technical breakthrough occurred that raised the profit per unit of *X* to $8, would this affect the optimal solution?

c. Instead of an increase in the profit coefficient *X* to $8, suppose that profit was overestimated and should only have been $3. Does this change the optimal solution?

2. 7-32 Consider the LP formulation given in Problem 7-31. If the second constraint is changed from 2X + 3Y≤2402X + 3Y≤240 to 2X+4Y≤240,2X+4Y≤240, what effect will this have on the optimal solution?

3. 7-33 The computer output given below is for Problem 7-31. Use this to answer the following questions.

a. How much could the profit on *X* increase or decrease without changing the values of *X* and *Y* in the optimal solution?

b. If the right-hand side of constraint 1 were increased by 1 unit, how much would the profit increase?

c. If the right-hand side of constraint 1 were increased by 10 units, how much would the profit increase?