Question

Find the maxium valve C=6x+2y. Subject to the following constraints x≥0, x≤5, y≥0, 4x-y≥1

Answer 1

The maximum value of C is 68

Explanation:

we have the following constraints

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

`x\leq 5` ----> constraint B

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

`4x-y\geq 1` ----> constraint D

Find out the area of the feasible region, using a graphing tool

The vertices of the feasible region are

(0,0),(5,19),(5,0)

see the attached figure

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

`C=6x+2y`

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

For (5,19) ----->
`C=6(5)+2(19)=68`

For (5,0) ----->
`C=6(5)+2(0)=30`

therefore

The maximum value of C is 68