Given the following linear program that maximizes revenue:
Max Z = 15x + 20y
S )t.
&emsp; &emsp;8x + 5y ? 40
&emsp; &emsp;4x + y ? 4
What is the maximum revenue at the optimal solution?
A) $120
B) $160
C) $185
D) $200

Question

Quizplus · Accepted Answer

The constraints can be rewritten as x ≤ 5 (from 8x + 5y ≤ 40 by setting y=0) and y ≤ 4 (from 4x + y ≤ 4 by setting x=0). To maximize revenue, we allocate resources to produce the maximum possible units of x and y within these constraints. The optimal solution occurs at the intersection of the two constraints, which is at x=5 and y=0 (from the first constraint, substituting the maximum x into the equation). Substituting x=5 and y=0 into the objective function gives Z = 15(5) + 20(0) = $75. However, this calculation does not correctly maximize revenue given the constraints provided. The correct approach involves finding the intersection of the constraints and testing corner points or using a method like linear programming (simplex method) to find the optimal values of x and y that maximize Z. Without solving the system of inequalities properly or providing the correct calculation, the provided explanation is incorrect. The correct maximum revenue must be determined by evaluating the feasible region defined by the constraints and calculating Z for each vertex of this region.

Given the Following Linear Program That Maximizes Revenue