calculus

Sam has 1200 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Express the area of the field as a function of its dimension. Find the dimensions of the field that has the largest area.

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  1. length parallel to river --- x ft
    each of other two sides -- y ft

    2x + y = 1200 ----> y = 1200 - 2x

    area = xy
    = x(1200-2x)
    = 1200x -2 x^2

    since you labeled it "Calculus"
    d(area)/dx = 1200 - 4x
    = 0 for a max of area
    4x = 1200
    x = 300

    width = 300
    length = 1200 - 2(300) = 600

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