Question

Linear programming subjected to constraints

Answer 1

Answer:

The maximum value of C is 14

Step-by-step 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