Consider the following LP problem developed at Zafar Malik’s Carbondale, Illinois, optical scanning firm:

Maximize profit = + 1X1 + $ 1X2

Subject to: 2X1 + 1X2 ≤ 100

1X1 + 2X2 ≤100

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 X1 to $ 3, would this affect the optimal solution?

c) Instead of an increase in the profit coefficient X1 to $ 3, sup-pose that profit was overestimated and should only have been $ 1.25. Does this change the optimal solution?