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calculus

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a farmer wishes to fence off a rectangular plot of land, using an existing wall as one of the sides . the total are enclosed must be 600 square yards. the fence on the side parallel to the wall will cost 20$ per yard, while the fences on the other side will cost 30$ per yard.

What should the dimension of the rectangle be in order to minimize the total cost of the fence?

  • calculus -

    let the two equal width be x
    let the single side by y

    xy = 600
    y = 600/x

    cost = 20y + 30x
    = 20(600/x) + 30x
    d(cost)/dx = -12000/x^2 + 30
    = 0 for a min of cost
    30 = 12000/x^2
    x^2 = 400
    x = 20

    the two equal sides are 20 yds each, and the long side is 600/20 = 30 yds.

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