# If the area shaded in Part A above represents the solution set to a linear programming problem. Show which combination within the set would maximize the objective function P = 10x + 8y, where P...

If the area shaded in P**art A** above represents the solution set to a linear programming problem. Show which combination within the set would maximize the objective function P = 10x + 8y, where P represent profit, and X and Yare the amount of good X and good Y respectively which the firm sells.

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### 1 Answer

The area shown has four boundaries. One of them is the line y/10 + x/5 = 1 => y = -2x + 1. The slope of this line is -2.

With each increment in x, the value of y decreases by 2.

The maximum value of P = 10x + 8y is at the point in the area where the value of x is maximum, this is (8, 1).

**The value of P is maximum at (8, 1)**