Find the values of x and y that maximize or minimize the objective function.

Question

x+y < or equal to 8
2x+y < or equal to 10
x> or equal to 0, y > or equal to 0

A. (0,5) Maximum value is 100
B.(1,7) Maximum value is 220
C.(2,6) Maximum value is 280
D. (5,0) Maximum value is 400

I'm so confused. Please help.

Answer 1

Sorry, I forgot to add the objective function.

C=80x+20y

Answer 2

Probably a little late, but this is how you solve it:

You are given two formulas:
x + y = 8
2x + y = 10

First manipulate them so that you have a common variable alone. I did:
y = 8 - x
y = 10 - 2x

Since y = y you can combine these formulas to create:
8 - x = 10 - 2x

Solve this to find x.
x = 2

Plug x into one of the original formulas:
(x) + y = 8
(2) + y = 8

Solve for y.
y = 6

You now have x and y.
(2,6)

Plug x and y into the objective function:
C = 80(x) + 20(y)
C = 80(2) + 20(6)

Solve for C.
C = 160 + 120
C = 280

You have your answer:
C.(2,6) Maximum value is 280