Question

Please help due before midnight I have no clue how to do this

Use graphical methods to solve the linear programming problem.
19) Maximize
z = 8x + 12y
subject to:
40x + 80y≤ 560
..
D
-10
10+
1
6x + 8y ≤72
x20
y20
A) Maximum of 96 when x = 9 and y = 2
B) Maximum of 92 when x = 4 and y = 5
C) Maximum of 100 when x = 8 and y = 3
D) Maximum of 120 when x = 3 and y = 8
+++>
10 x

Answer 1

The maximum value of the objective function is 100 when x = 8 and y = 3

How to find the maximum value of the objective function

From the question, we have the following parameters that can be used in our computation:

Max z = 8x + 12y

Subject to:

40x + 80y ≤ 560

6x + 8y ≤72

Plot the grah of the constraints (see attachment)

From the graph, we have the feasible coordinates to be

(x, y) = (8, 3), (12, 0) and (0, 7)

Recall that

Max z = 8x + 12y

So, we have

z(8, 3) = 8 * 8 + 12 * 3 = 100

z(12, 0) = 8 * 12 + 12 * 0 = 96

z(0, 7) = 8 * 0 + 12 * 7 = 84

The maximum of these values is 100

Hence, the maximum value of the objective function is 100