Question

2. Given the objective function C=3x−2y and constraints x≥0, y≥0, 2x+y≤10, 3x+2y≤18, find the maximum value of C. (2.0 Points)

Answer 1

The maximum value of C is 15

Explanation:

we have

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

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

`2x+y\leq 10` -----> constraint C

`3x+2y\leq 18` -----> constraint D

using a graphing tool

The solution area of the constraints in the attached figure

we have the vertices

(0,0),(0,9),(2,6),(5,0)

Substitute the value of x and the value of y in the objective function

(0,0) ----->
`C=3(0)-2(0)=0`

(0,9) ----->
`C=3(0)-2(9)=-18`

(2,6) ----->
`C=3(2)-2(6)=-6`

(5,0) ----->
`C=3(5)-2(0)=15`

therefore

The maximum value of C is 15