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An ostrich farmer wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. There are 720 feet of fencing available to complete the job. What is the largest possible total area of the 4 pens?

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Leah
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  1. let the width of one of the pens be x, let its length be y

    so we have 8x + 5y = 720
    y = (720 - 8x)/5 = 144 - 8x/5

    area = 4xy
    = 4x(144 - 8x/5)
    = 576x - (32/5)x^2

    d(area)/dx = 576 - 64x/5
    = 0 for a max of area
    64x/5 = 576
    64x = 2880
    x = 45

    largest total area = 4(45)(144 - 8(45)/5)
    = 12960 ft^2

    check my arithmetic

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    Reiny

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