Question

Linear programming subjected to constraints

Answer 1

The maximum value of C is 14

Explanation:

we have the following constraints

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

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

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

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

Determine the area of the feasible region using a graphing tool

see the attached figure

The vertices of the feasible region are

`(0,0),(0,5),(2,3),(3,0)`

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

we have

`C=4x+2y`

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

For (0,5) ---->
`C=4(0)+2(5)=10`

For (2,3) ---->
`C=4(2)+2(3)=14`

For (3,0) ---->
`C=4(3)+2(0)=12`

therefore

The maximum value of C is 14