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Math Help - Max and Min values question.

  1. #1
    Harne
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    Max and Min values question.

    A local furniture manufacturer sells cedar pato sets. The company can sell x units each month at a price of p(x)=1000-x in dollars, where the cost, C, of producing x units per day is, C(x)=3000+19x^2.

    Determine a) the price that will maximize the profits
    and b) the break even point.

    Not sure where to start...
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Harne View Post
    A local furniture manufacturer sells cedar pato sets. The company can sell x units each month at a price of p(x)=1000-x in dollars, where the cost, C, of producing x units per day is, C(x)=3000+19x^2.

    Determine a) the price that will maximize the profits
    and b) the break even point.

    Not sure where to start...
    Lets see, we sell at  1000 - x BUT the cost to produce it is  3000 + 19x^2

    So wouldn't the profit be  1000 - x - (3000 + 19x^2)

    So find the derivative of x in the profit formula and set x into the price formula.
    Last edited by janvdl; May 23rd 2007 at 10:52 AM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by janvdl View Post
    Lets see, we sell at  1000 - x BUT the cost to produce it is  3000 + 19x^2

    So wouldn't the profit be  1000 - x - (3000 + 19x^2)

    So find the derivative of x in the profit formula and set x into the price formula.
    No the sales are 1000-x units per day when the price per unit is x, so
    the revenue is (1000-x)x, and the cost to produce x units is 3000+19x^2.

    So the profit is:

    1000x - x^2 -3000 - 19x^2 = -20x^2+1000x -3000.

    RonL
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  4. #4
    Bar0n janvdl's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    No the sales are 1000-x units per day when the price per unit is x, so
    the revenue is (1000-x)x, and the cost to produce x units is 3000+19x^2.

    So the profit is:

    1000x - x^2 -3000 - 19x^2 = -20x^2+1000x -3000.

    RonL
    Ah ok, didnt realise that i should have multiplied with an extra  x
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