Question

Finding binomial values ​​graphically

MAX Z = 5x1 + 4x2
subject to
2x1 + 5x2 <= 34
x1 + x2 <= 18
x1 + 8x2 <= 24
x1 - 4x2 >= 2
and x1,x2 >= 0

Answer 1

A graph of the constraint region is shown in the image below.

The maximum value of the objective function is 85.

In this exercise, we would graph the feasible region that is defined by the constraints and then, we would evaluate the objective function (Z) at these vertices of the feasible region in order to find the maximum value.

Based on the points where the shaded regions overlap in the graph, we have the following vertices of the feasible region:

(152/11, 14/11), (17, 0), (0, 3), (0, 1/2), and (2, 0).

Now, we can evaluate the objective function
`Z=5x_1+4x_2` at these vertices as follows.

For (152/11, 14/11), we have;

Z = 5(152/11) + 4(14/11)

Z = 816/11

Z = 74.1818

For (17, 0), we have;

Z = 5(17) + 4(0)

Z = 85

For (0, 3), we have;

Z = 5(0)+ 4(3)

Z = 12

For (0, 1/2), we have;

Z = 5(0)+ 4(1/2)

Z = 2

For (2, 0), we have;

Z = 5(2) + 4(0)

Z = 10