Geometry

A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and 115 feet of fencing for the remaining 3 sides. What dimensions will give her the maximum area for the pen?

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  1. if the pen has dimensions x by y, with x along the barn, then

    x+2y = 115

    the area a is thus

    a = xy = (115-2y)y

    this is a parabola, with maximum at y=115/4

    so, x = 115/2

    so, a pen 115/4 by 115/2 gives the maximum area

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