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calculus (optimization)

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a rectangular study area is to be enclosed by a fence and divided into two equal parts, with the fence running along the division parallel to one of the sides. if the total area is 384 square feet, find the dimensions of the study area that will minimize the total length of the fence. how much fencing will be required?

  • calculus (optimization) - ,

    xy=384
    so, y = 384/x

    f = 2x+3y = 2x + 1152/x
    df/dx = 2 - 1152/x^2
    min f is when df/dx=0, at x=24

    So, the field is 24x16
    f = 48+48=96

    as usual in these problems, the fencing is divided equally among lengths and widths.

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