Question

What point in the feasible region maximizes the objective function?

Constraints: x >= 0, y >= 0, y <= 3, y <= 2x + 5
Objective function: C = -6x + 5y
A. (0,0)
B. (1,4)
C. (0,3)
D. (5/2,0)

Answer 1

To find the point in the feasible region that maximizes the objective function, evaluate the objective function at each corner point of the feasible region. The point (1,3) maximizes the objective function.

Step-by-step explanation:

The feasible region represents the set of points that satisfy all the given constraints. To find the point in the feasible region that maximizes the objective function, we need to evaluate the objective function at each corner point.

The corner points of the feasible region are (0,0), (1,3), and (5/2,0). Evaluating the objective function at each of these points, we get:

For (0,0): C = -6(0) + 5(0) = 0

For (1,3): C = -6(1) + 5(3) = -6 + 15 = 9

For (5/2,0): C = -6(5/2) + 5(0) = -15/2 + 0 = -15/2

Therefore, the point in the feasible region that maximizes the objective function is (1,3) which corresponds to option B.