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Math Help - Did i do this right

  1. #1
    Newbie
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    Question Did i do this right

    A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

    let the sides by x and y. then xy = 500000, so y = 500000/x

    the length you want to minimize is f(x) = 3x + 2y (because of the extra bit down the middle)
    f(x) = 3x + 1000000/x

    to find the optimal length, solve df/dx = 0

    df/dx = 3 - 1000000/x^2 = 0
    i.e., solve 3 = 1000000/x^2
    x^2 = 1000000 / 3
    x = 1000 / sqrt(3)

    shortest total length is f(1000 / sqrt(3))
    = 3000 / sqrt(3) + 1000 sqrt(3)
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  2. #2
    A Plied Mathematician
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    Your answer looks correct to me. You can simplify your final answer a little bit by adding the fractions.
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