Question

Given constraints: x>=0, y>=0, 2x+2y>=4, x+y<=8 explain the steps for maximizing the objective function P=3x+4y.

Answer 1

Graph the inequalities given by the set of constraints. Find points where the boundary lines intersect to form a polygon. Substitute the coordinates of each point into the objective function and find the one that results in the largest value.

Explanation:

the sample answer

Answer 2

The maximum value of P is 32

Explanation:

we have following constraints

`x\geq 0` ----> constraint A

`y\geq 0` ----> constraint B

`2x+2y\geq 4` ----> constraint C

`x+y\leq 8` ----> constraint D

Solve the feasible region by graphing

using a graphing tool

The vertices of the feasible region are

(0,2),(0,8),(8,0),(2,0)

see the attached figure

To find out the maximum value of the objective function P, substitute the value of x and the value of y of each vertex of the feasible region in the objective function P and then compare the results

we have

`P=3x+4y`

so

For (0,2) --->
`P=3(0)+4(2)=8`

For (0,8) --->
`P=3(0)+4(8)=32`

For (8,0) --->
`P=3(8)+4(0)=24`

For (2,0) --->
`P=3(2)+4(0)=6`

therefore

The maximum value of P is 32