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Math Help - Growth - please help check my answers

  1. #1
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    Growth - please help check my answers

    A property developer is planning to build houses on 4 acres of land. She estimates that if she builds 16 houses, the profit per house will be $400,000, and that each additional house she builds will reduce her profit per house by $10,000. The total profit P(n), in thousands of dollars, from making n houses, can be modelled by the function:

    Code:
    P(n)= 560n-10n^2
    
    (a) How much profit will the developer make from making 9 houses according to this
    model?
    $4, 230, 000



    (b) Find the roots of the equation P(n) = 0, and use these to find how many houses the developer should build for maximum profit. State the value of this profit.

    The roots are when n = 0 or 56
    build 28 houses for maximum profit
    $7,840,000 is the value of the profit if the developer builds 28 houses


    (c) What is a sensible practical domain for P(n)?
    starts with n = 0 – can’t have negative number of houses and ends with n= 28 – as this is the maximum value of P(n), after this the profit starts decreasing.
    Code:
    0<= n <= 28
    (d) The developer needs to make at least $6,800,000 (i.e. $6800 thousand) to invest in a block of land she wishes to purchase for her next development project. Find algebraically the roots of the equation P(n) = 6800, and use your answer to suggest how many houses she needs to build to gain this much profit.

    Code:
     560n-10n^2 -6800 = 0
    
    n = 17.80196097 or 38.19803903


    She should build 38 houses to make at least $6,800,000




    I'm sorry I didn't include my working, but its quiet difficult to type it all out. Any assistance with this would be great, thanks for looking
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  2. #2
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    Dec 2008
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    (d) The developer needs to make at least $6,800,000 (i.e. $6800 thousand) to invest in a block of land she wishes to purchase for her next development project. Find algebraically the roots of the equation P(n) = 6800, and use your answer to suggest how many houses she needs to build to gain this much profit.

    Code:
    560n-10n^2 -6800 = 0

    n = 17.80196097 or 38.19803903


    She should build 38 houses to make at least $6,800,000
    if i get this right.. to make at least $6,800,000 she should build at least 18 houses, but not more than 38.

    17 < houses built < 39 => at least $6,800,000

    other answers are correct.
    Last edited by mr fantastic; January 24th 2009 at 01:26 PM. Reason: Merged posts
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  3. #3
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    Thanks metlx

    Hey metlx,

    Thanks for your response! I've use the thank you button on you
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