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Math Help - Optimization problem

  1. #1
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    Optimization problem

    Find 2 positive numbers whose product is 110 and the sum of the first plus twice the second is a minimum.

    This problem is really confusing. Any help greatly appreciated.
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  2. #2
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    Quote Originally Posted by av8or91 View Post
    Find 2 positive numbers whose product is 110 and the sum of the first plus twice the second is a minimum.

    This problem is really confusing. Any help greatly appreciated.

    xy=110

    x+2y=minimum

    Write one value in terms of the other.

    y=\frac{110}{x}

    Then substitute to obtain an equation in one variable.

    x+2\frac{110}{x}=x+\frac{220}{x}=x+220x^{-1}

    Now, differentiate this and find the x for which the derivative is zero.
    This gives the value of x corresponding to the minimum value of x+2y=110.
    Then use this x to find y.
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