Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

What point in the feasible region maximizes the objective function?

Constraints:
x ≥ 0
y ≥ 0
−x + 3 ≥ y
y ≤ 1/3x + 1
Objective function:
C = 5x – 4y

Answer 1

The point that maximizes the objective function is (3,0)

Explanation:

we have

Constraints:

`x\geq 0\\y\geq 0\\-x + 3\geq y\\y\leq (1)/(3)x+1`

Using a graphing tool

The feasible region is the shaded area

see the attached figure

The vertices of the feasible region are

(0,0),(0,1),(1.5,1.5) and (3,0)

we know that

To find the point in the feasible region that maximizes the objective function, replace each ordered pair of vertices in the objective function and then compare the results.

The objective function is

`C=5x-4y`

For (0,0) ----->
`C=5(0)-4(0)=0`

For (0,1) ----->
`C=5(0)-4(1)=-4`

For (1.5,1.5) ----->
`C=5(1.5)-4(1.5)=1.5`

For (3,0) ----->
`C=5(3)-4(0)=15`

therefore

The point that maximizes the objective function is (3,0)