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if a farmer has 100 feet of fence and wants to make a rectangular pigpen, one side of which is along existing straight fence.What dimensions should be used in order to maximize the area of the pen?

  • calculus -

    25 - 25 - 50
    Maximum Area = 1250 ft^2

    How to get that answer:
    Let x be the side length that is used twice. The side parallel to the existing fence then has length 100 - 2x.
    The area A is then

    A(x) = x*(100 - 2x) = 100 x - 2x^2
    dA/dx = 0 when
    100 = 4x
    x = 25

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