Reference no: EM132514565

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.

The corner point and profits are:

X= 0, Y=0, profit 0

X=60, Y=0, profit= 300

X=30, Y=60, profit= 510

X=0, Y= 80, profit= 480

The optimal point is (30,60) in which you will earn the maximum profit.

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

If profit= 8X+6Y, the optimal solution is at the same corner point but profit increases.

X=0, Y=0 profit=0

X=60, Y=0, profit= 480

X=30, Y=60, profit= 600

X=0, Y= 80, profit= 480

The optimal solution is at the point (30,60).