Question

Given this LP Model below:

Max Z = 4x + 5y

Subject to

2x + 2y <= 22

-1x + 1y <= 4

y <= 7

1x - 5y <= 0

x >= 0, y >= 0

a) Solve for the quantities of x and y which will maximize Z. The x =Blank 1. The y = Blank 2.

b) What is the maximum value of Z? The Z = Blank 3.

Answer 1

Answer and Explanation:

a) To find the quantities of x and y that maximize Z, we need to evaluate the objective function at the vertices of the feasible region.

The vertices of the feasible region are:

A: (0, 0)

B: (0, 4)

C: (3, 4)

D: (8, 2)

E: (11, 0)

Evaluating Z at each vertex:

Z_A = 4(0) + 5(0) = 0

Z_B = 4(0) + 5(4) = 20

Z_C = 4(3) + 5(4) = 32

Z_D = 4(8) + 5(2) = 44

Z_E = 4(11) + 5(0) = 44

b) The maximum value of Z is 44.

Therefore:

a) The value of x that maximizes Z is 8.

b) The value of y that maximizes Z is 2.

c) The maximum value of Z is 44.