What combination of x and y will yield the optimum for this problem?
Maximize $3x + $15y, subject to (1) 2x + 4y

Question

What combination of x and y will yield the optimum for this problem?
Maximize $3x + $15y, subject to (1) 2x + 4y < 12 and (2) 5x + 2y < 10 and (3) x, y ≥ 0.
A) x = 2, y = 0
B) x = 0, y = 3
C) x = 0, y = 0
D) x = 1, y = 5
E) none of the above

Quizplus · Accepted Answer

To find the optimum, we can graph the constraints and identify the feasible region. The objective function is maximized at a vertex of the feasible region. Testing the vertices (which are the intersections of the constraints), we find that the option B (x = 0, y = 3) satisfies all constraints and maximizes the objective function $3x + $15y, yielding the maximum value of $45.

What Combination of X and Y Will Yield the Optimum