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Math Help - Help finding optimal proposal for housing project with a funding limit

  1. #1
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    Help finding optimal proposal for housing project with a funding limit

    There are 2 proposals for a housing project.
    x is measured in hundreds of units, and Average Cost(AC) is measured in thousands of dollars

    proposal 1

    AC1 = x^2 4x + 6
    proposal 2

    AC2 = x^3/3 3x^2 + 8x + 2


    c) What is the optimal proposal if they can spend no more than $3,000,000?




    Using my graphing calculator i found that proposal 1 can build 424 units at an AC of $7017.60 (4.24,7.0176)without going over 30mil and proposal 2 can build 408 at an AC of $7339.90

    (4.08,7.339904)


    Obviously proposal 1 is better, but how can i show this on paper in proper mathematical format? Help please!!!
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  2. #2
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    Quote Originally Posted by seanP View Post
    There are 2 proposals for a housing project.
    x is measured in hundreds of units, and Average Cost(AC) is measured in thousands of dollars

    proposal 1

    AC1 = x^2 – 4x + 6
    proposal 2

    AC2 = x^3/3 – 3x^2 + 8x + 2


    c) What is the optimal proposal if they can spend no more than $3,000,000?




    Using my graphing calculator i found that proposal 1 can build 424 units at an AC of $7017.60 (4.24,7.0176)without going over 30mil and proposal 2 can build 408 at an AC of $7339.90

    (4.08,7.339904)


    Obviously proposal 1 is better, but how can i show this on paper in proper mathematical format? Help please!!!
    Substitute AC = 3\,000\,000 into each equation and solve each for x.
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