Question

Given constraints: x>=0, y>=0, 2x+2y>=4, x+y<=8 explain the steps for maximizing the objective function P=3x+4y.

Answer 1

Answer:

The maximum value of P is 32

Step-by-step explanation:

we have following constraints

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

$y\geq 0$ ----> constraint B  

$2x+2y\geq 4$ ----> constraint C

$x+y\leq 8$ ----> constraint D

Solve the feasible region by graphing

using a graphing tool

The vertices of the feasible region are

(0,2),(0,8),(8,0),(2,0)

see the attached figure

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

we have

$P=3x+4y$

so

For (0,2) ---> $P=3(0)+4(2)=8$

For (0,8) ---> $P=3(0)+4(8)=32$

For (8,0) ---> $P=3(8)+4(0)=24$

For (2,0) ---> $P=3(2)+4(0)=6$

therefore

The maximum value of P is 32

Answer 2

Answer:

Graph the inequalities given by the set of constraints. Find points where the boundary lines intersect to form a polygon. Substitute the coordinates of each point into the objective function and find the one that results in the largest value.

Step-by-step explanation:   that is the answer on edg.