Question

Find the maximum value of p=3x+2y subject to the following constraints 5x+y<16

2x+3y<22
x>0
y>0

Answer 1

The maximum value of p is 18

Explanation:

we have

`5x+y \leq16` ------> constraint A

`2x+3y \leq22` ----> 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), (0,7.3), (2,6) and (3.2,0)

To find the maximum value of p, substitute the value of x and the value of y of each vertices in the equation and then compare the results

`p=3x+2y`

For (0,0)

`p=3(0)+2(0)=0`

For (0,7.3)

`p=3(0)+2(7.3)=14.6`

For (2,6)

`p=3(2)+2(6)=18`

For (3.2,0)

`p=3(3.2)+2(0)=9.6`

therefore

The maximum value of p is 18