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Math Help - Maximum profit question

  1. #1
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    Maximum profit question

    it costs you 10 euros per backpack to manufacture and distribute backpacks.if the backpacks sell at x euros each (where 15=or< x=or<100) the number sold is given by
    n=a/x-10+b(100-x),
    where a and b are positive constants.what selling price will bring a maximum profit?
    Last edited by CaptainBlack; July 16th 2011 at 10:38 PM.
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  2. #2
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    Re: maths help!!!!!!!!!!!!!!!!!!!!

    What have you tried here?

    To find a maximum with these types of problems often require you finding a derivative and solving for the zeros.
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  3. #3
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    Re: Maximum profit question

    Quote Originally Posted by university View Post
    it costs you 10 euros per backpack to manufacture and distribute backpacks.if the backpacks sell at x euros each (where 15=or< x=or<100) the number sold is given by
    n=a/x-10+b(100-x),
    where a and b are positive constants.what selling price will bring a maximum profit?
    Profit = price*number sold - cost of production

    In this case x is the cost of producing one unit so the cost of produceing n units is x\times n, so you end up with and the profit on one unit is (x-10):

    Profit= (x-10)\left[\frac{a}{x-10}+b(100-x)\right] -10x

    Now when you simplify the right hand side of the above you will end up with a quadratic expression in x, and you have to find the maximum of this subject to the constraints on x.

    (the last part can be done without calculus by completing the square)

    CB
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  4. #4
    Grand Panjandrum
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    Re: maths help!!!!!!!!!!!!!!!!!!!!

    Quote Originally Posted by pickslides View Post
    What have you tried here?

    To find a maximum with these types of problems often require you finding a derivative and solving for the zeros.
    This is a problem in finding the maximum of a quadratic, no calculus required.

    CB
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