Posted by **LaH** on Wednesday, October 26, 2011 at 6:50pm.

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

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.

- Algebra 2 -Linear Programming -
**LaH**, Wednesday, October 26, 2011 at 7:12pm
Sorry, I forgot to add the objective function.

C=80x+20y

- Algebra 2 -Linear Programming -
**Bill G**, Friday, October 28, 2011 at 10:16am
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

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