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25 April, 14:23

A financier plans to invest up to $600,000 in two projects. Project A yields a return of 9% on the investment x dollars, whereas project B yields a return of 16% on the investment of y dollars. Because investment B is riskier than investment 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 to maximize the return on her investment P in dollars, and what amount is available for investment?

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  1. 25 April, 17:52
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    Project A = $240,000

    Project B = $360,000

    Explanation:

    Planned Investment amount = $600,000

    Project A = x dollars, with 9% return

    Project B = Y dollars, with 16% return

    Project B should not exceed 40% of total investment amount

    Therefore, if y dollars is spent on project B,

    (600,000 - y) is spent on project A

    Return on project A:

    0.09 (600,000 - y) = 54,000 - 0.09y

    Return on project B:

    0.16y

    Total return = return on A + return on B

    54,000 - 0.09y + 0.16y

    Total return = 54,000 + 0.07y

    Note: Project B should not exceed 40% of investment, Therefore,

    y < = 0.4 (600,000)

    y < = 240,000

    slope of the function is positive '54,000 + 0.07y', total return increases when y increases.

    Therefore return on investment will be maximized when y = 240,000, as it should not exceed 40% for project B and the rest 360,000 can be invested in project A.
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