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Calculus

a college is planning to construct a new parking lot. the parking lot must be rectangular and enclose 6000 square meters of land. A fence will surround the parking lot, and another fence parallel to one of the sides will divide the parking lot into two sections, what are the dimension in meters of the rectangular lot that uses the least amount of fencing?

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  1. w x = 6000 so w = 6000/x

    L = 3 w + 2 x

    L = 18000/x + 2 x

    dL/dx = -18000/x^2 + 2 x = 0 for max or min

    2x = 18,000/x^2
    x^3 = 9,000
    x = 20.8
    w = 288.4

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  2. A = w x = 6000 so w = 6000/x

    L = 3w + 2x

    L = 18000/x + 2x

    dL/dx = (-18000/x^2) + 2 = 0 for max or min

    2 = 18,000/x^2
    x^2 = 9,000
    x = 30*sqrt(10)
    w = 20*sqrt(10)

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