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

Respuesta :

calculista

Answer:

The maximum value of P is 32

Step-by-step explanation:

we have following constraints

[tex]x\geq 0[/tex] ----> constraint A

[tex]y\geq 0[/tex] ----> constraint B  

[tex]2x+2y\geq 4[/tex] ----> constraint C

[tex]x+y\leq 8[/tex] ----> 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

[tex]P=3x+4y[/tex]

so

For (0,2) ---> [tex]P=3(0)+4(2)=8[/tex]

For (0,8) ---> [tex]P=3(0)+4(8)=32[/tex]

For (8,0) ---> [tex]P=3(8)+4(0)=24[/tex]

For (2,0) ---> [tex]P=3(2)+4(0)=6[/tex]

therefore

The maximum value of P is 32

Ver imagen calculista
kaitlynmeats

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.

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