Question

Your friend is trying to find the maximum value of P = -x + 3y subject to the following four constraints.

• What error did your friend make in the graph below?

• What is the correct solution?

Answer 1

The maximum value of P=11 occurs at x=1 and y=4

Explanation:

we have

`y\leq -2x+6` ----> constraint A

`y\leq x+3` ----> constraint B

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

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

using a graphing tool

The solution is the shaded area

see the attached figure

The vertices of the solution area are

(0,0),(0,3),(1,4),(3,0)

Substitute the value of x and the value of y of each vertex in the objective function , to find out the maximum value of P

The objective function is

`P=-x+3y`

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

For (0,3) ----->
`P=-(0)+3(3)=9`

For (1,4) ----->
`P=-(1)+3(4)=11`

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

therefore

The maximum value of P=11 occurs at x=1 and y=4