Question

Please help me out with this problem!!!!!!

Answer 1

The minimum value of C is 6, for x=0 and y=2

Explanation:

we have the following constraints

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

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

`2x+3y\geq 6` ---> constraint C

`3x-2y \leq 9` ---> constraint D

`x+5y\leq 20` ---> constraint E

using a graphing tool

Find out the feasible region

The feasible region is the shaded area

see the attached figure

The vertex of the feasible region are

(0,2),(0,4),(5,3) and (3,0)

The objective function is

`C=4x+3y`

To find out the minimum value, substitute the value of x and the value of y of each vertices in the objective function and then compare the results

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

For (0,4) --->
`C=4(0)+3(4)=12`

For (5,3) --->
`C=4(5)+3(3)=29`

For (3,0) --->
`C=4(3)+3(0)=12`

therefore

The minimum value of C is 6, for x=0 and y=2