Question

Find the maximum value of P=3x+2y subject to the following constraints:
Please help!!!

Answer 1

The maximum value of P is 18

Explanation:

we have'the constraints

`5x+y\leq 16` ---> constraint A

`2x+3y\leq 22` ---> constraint B

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

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

using a graphing tool

The solution of the four constraints is the quadrilateral shaded area

The vertices of the quadrilateral area are

(0,0),(3.2,0),(2,6) and (0,7.33)

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 in the objective function and then compare the results

so

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

For (3.2,0) ---->
`P=3(3.2)+2(0)=9.6`

For (2,6) ---->
`P=3(2)+2(6)=18`

For (0,7.33) ---->
`P=3(0)+2(7.33)=14.66`

therefore

The maximum value of P is 18