7.7problems (3)

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.