A financier plans to invest up to $500,000 in two projects. Project A yields a return of 11% on the investment of x dollars, whereas Project B yields a return of 16% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, she has decided that the investment in Project B should not exceed 40% of the total investment. How much should the financier invest in each project in order to maximize the return on her investment?

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  1. You want to maximize
    p = 0.11x + 0.16y subject to
    x+y = 500000
    y <= 0.40(x+y)

    So, graph the region and pick the vertex which maximizes the income.

    I get (in 10,000's) p(30,20) = 6.50

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