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Thread: max/min on an interval #1

  1. #1
    Senior Member
    Nov 2008

    max/min on an interval #1

    In a certain manufacturing process, when the level of production is x units, the cost of production in dollars, is C(x)=3000+9x+0.05x^2, 1<=x<=300. What level of production x will minimize the unit cost U(x)=C(x)/x? Keep in mind that the production level must be an integer.

    This is my work below.. it conflicts with the back of the book again. My answer is 34 and they have 245......





    therefore the cost of production level should be 10200 dollars at 300 units or 34 dollars per unit.

    so, is mine wrong and what did i do wrong?
    Last edited by mr fantastic; Aug 12th 2009 at 03:53 PM. Reason: Changed post title
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  2. #2
    MHF Contributor
    skeeter's Avatar
    Jun 2008
    North Texas
    you're minimizing U(x) , not C(x).

    U(x) = C(x)/x = 3000/x + 9 + 0.05x

    U'(x) = -3000/x^2 + 0.05

    U'(x) = 0 when x is approx 245.
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