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A farmer has 2,400 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Write the function that will produce the largest area if x is the short side of the rectangle.

  • Math -

    2x+y = 2400
    so, y = 2400-2x

    a = xy = x(2400-2x) = 2400x-2x^2
    That is just a parabola, with vertex at x=600

    So, the field is 600 x 1200

    As usual, these problems achieve maximum area when the perimeter is divided equally among lengths and widths.

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