Question

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

Answer 1

Answer:

The maximum value of C is 68

Step-by-step 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