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Math Help - Optimization Problem

  1. #1
    Junior Member
    Joined
    Sep 2007
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    56

    Optimization Problem

    Hi this is the problem i'm having trouble with.

    Find two numbers whose difference is 100 and whose product is minimum.



    I don't even know where to start on this one. Thanks guys.
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  2. #2
    Junior Member
    Joined
    Nov 2008
    Posts
    44

    Optimization Problem

    It seems like you'll need two numbers that differ by 100, which we'll call X and X-100. You want the minimum product of these two numbers, which means you'll want the derivative of the function X * (X - 100).

    NOte that X * (X - 100) = X^2 - 100X, which is easier to differentiate. It results in a derivative of 2X - 100.

    To find the mminimum, set this equation equal to 0, and you'll get
    2X - 100 = 0 ===> X = 50. So your two numbers would be 50 and -50, with a minimum product of 50 * -50 = -2,500.

    - Steve J
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