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Math Help - Linear programming?

  1. #1
    Newbie Almondzqueen's Avatar
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    Linear programming?

    A financier plans to invest up to $500,000 in two projects. Project A yields a return of 10% on the investment whereas project B yields a return of 15% on the investment. Because the investment in project B is riskier than the investment in Project A, the financier has decided that the investment in Project B should not exceed 40% of the total investment. How much should she invest in each project in order to maximize the return on her investment? What is the maximum return?

    I need help with this problem. I have set up:
    max P= .10x +.15y
    subj to: x+y ≤ 500,000
    y <= 200,000
    x, y >= 0

    My professor says the constraint y ≤ 200,000 is not correct. It's supposed to be something like y<= .4 (x+y)?
    I am completely confused, can someone help me clear this constraint up?
    thanks.
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Define x to be the amount invested in project A and y to be the amount invested in project B

    Consider that you may not invest the entire amount as your first constraint implies.
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  3. #3
    Newbie Almondzqueen's Avatar
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    would it be y ≤ .4 (x+y)
    y≤ 24000? i need to graph this as well.
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