Question

What point in the feasible region maximizes the objective function?

Constraints:

x ≥ 0

y ≥ 0

− x + 3 ≥ y

y ≤ 1/3 x + 1

Objective function: C =5x-4y

Answer 1

Answer:

(3,0)

Step-by-step explanation:

Observe the image. The feasible region ( shaded region) is the intersection of the inequalities of the problem.

For find an optimal solution we think as follow. We consider the set of all points whose objective function $-5x-4y$ is equal to z. This is the doted purple line in the image. Observe that this line is perpendicular to the vector $c=(5,-4)$ (blue vector) and note that increasing z correspond to moving the line $z=5x-4y$ in direction of the vector c. Since we need increase the value of the objective function, we would like to move the line as much as possible in the direction of the vector c without leave the feasible region.

Watching the image we observe that the best we can do is z=15, and the line pass by the vertex of the feasible region (3,0).

Then the point (3,0) maximizes the objective function.