Question

Use graphical methods to solve the linear programming problem.

40x + 80y ≤ 560.
6x + 8y ≤ 72.
x ≥ 0.
y ≥ 0.
Maximize P = 8x + 12y

A. Maximum of 92 when x = 4 and y = 5

B. Maximum of 96 when x = 9 and y = 2

C. Maximum of 100 when x = 8 and y = 3

D. Maximum of 120 when x = 3 and y = 8

Answer 1

I would substitute each and every option and see if it satisfies. ex. P= 8(3)+12(8)= 96+24=120 (check) but it fails to satisfy 40x+80y=560, etc...

Answer 2

If you want to solve this graphically, you need to draw two axis, X and Y. In these axis you display the four equations that you've listed, where you've replaced the inequality with equality, so 40x+80y=560.

For each line that you've drawn, you have to determine which part of the graph suits your constraint. Mark that part with a color or so.

Your solution is the area which has four colors, meaning: the area which is valid for all of the four equations. See the drawing for the graphical approach.