calculus optimization problem

A farmer has 460 feet of fencing with which to enclose a rectangular grazing pen next to a barn. The farmer will use the barn as one side of the pen, and will use the fencing for the other three sides. find the dimension of the pen with the maximum area?

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  1. L + 2 W = 460
    so
    L = (460 - 2 W)

    L * W = A
    A = (460-2W)W = 460 W - 2 W^2
    DA/DW = 460 - 4 W
    ZERO FOR MAX OR MIN
    4 W = 460
    W = 115

    L = 460 - 2*115 = 230

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