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Algebra 2 -Linear Programming

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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 - ,

    Sorry, I forgot to add the objective function.

    C=80x+20y

  • Algebra 2 -Linear Programming - ,

    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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