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Math Help - Boxes of Candy

  1. #1
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    Boxes of Candy

    The monthly revenue achieved by selling x boxes of candy is figured to be
    x(5 - 0.05x) dollars. The wholesale cost of each box of candy is $1.50. How many boxes must be sold each month to achieve a profit of at least $60?

    What about if the question asked:

    How many boxes must be sold each month to achieve a profit of at most $60?

    In terms of inequality word problems, what is the difference between at least and at most questions?

    Thanks
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  2. #2
    MHF Contributor Quick's Avatar
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    To say x is at least 50, you would write: x\geq 50

    To say at most 50 you would write: x\leq 50
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  3. #3
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    ok

    Great information given but what are the steps for me to find the answer?

    Can you set up an equation?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    The monthly revenue achieved by selling x boxes of candy is figured to be
    x(5 - 0.05x) dollars. The wholesale cost of each box of candy is $1.50. How many boxes must be sold each month to achieve a profit of at least $60?
    Profit is revenue-costs, so in this case:

    p=x(5-0.05x) - 1.5x=-0.05 x^2 + 3.5 x

    we want this to be at least 60 dollars, so we want p>=60.

    Now as p is a quadratic in x, with a negative coefficient to the x^2 term
    p>=60 between the roots of:

    p=-0.05x^2+3.5x =60

    or between the roots of 0.05 x^2-3.5 x +60=0.

    The roots of this quadratic are 30 and 40, so the profit >=$60, for
    30<=x<=40.

    RonL
    Last edited by CaptainBlack; January 14th 2007 at 06:19 AM.
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  5. #5
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    ok

    To poster QUICK:

    Where did you get 50?

    The question deals with 60, right?
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