# Question

Consider the following LP problem developed at Jeff Spencer’s San Antonio optical scanning firm:

Maximize profit = $1X1 + $1X2

Subject to: 2X1 + 1X2 ≤ 100

1X1 + 2X1 ≤ 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, suppose that profit was overestimated and should only have been $1.25. Does this change the optimal solution?

Maximize profit = $1X1 + $1X2

Subject to: 2X1 + 1X2 ≤ 100

1X1 + 2X1 ≤ 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, suppose that profit was overestimated and should only have been $1.25. Does this change the optimal solution?

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