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Math Help - Alegebra shirt sales problem

  1. #1
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    need help please!

    A company makes and ships their backpacks at $5 each.If the backpacks sell for $p each,the number sold ,x, is given by x=a/(p-10)+b(130-p),where a and b are constants.what selling price will yield the largest profit for the company
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bobby77
    A company makes and ships their backpacks at $5 each.If the backpacks sell for $p each,the number sold ,x, is given by x=a/(p-10)+b(130-p),where a and b are constants.what selling price will yield the largest profit for the company
    This looks peculiar, as your sales are \infty when the selling price is $10.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by bobby77
    A company makes and ships their backpacks at $5 each.If the backpacks sell for $p each,the number sold ,x, is given by x=a/(p-10)+b(130-p),where a and b are constants.what selling price will yield the largest profit for the company
    Lets assume that the sales should be:

     x= \frac{a}{p+10}+b(130-p)

    The profit per sale is:

    p-5

    so the total profit is:

    P=(p-5).x=(p-5). \left\{\frac{a}{p+10}+b(130-p)\right\}

    Now the usual way to find the maximum total profit is to differentiate P wrt
    the price p and then set the result to zero. Then solve for the price which
    maximises the profit. Which is what you have to do here.

    You should normaly check that the solution/s is/are maxima or minima just
    to be sure.

    RonL
    Last edited by CaptainBlack; December 17th 2005 at 11:04 PM.
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