# Calculating optimal solution

Consider the following LP problem:

Maximize profit = 5x + 6y

subject to 2x + y < 120

2x + 3y < 240

x,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 coefficent x to $8, suppose that profit was overestimated and should have only been $3. Does this change the optimal solution?

Consider the above LP formulation. if the second constraint is changed from 2x + 3y <240 to 2x + 4y < 240, what affect will this have on the optimal solution?

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