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Calc.

A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $7 a foot, while the remaining two sides will use standard fencing selling for $2 a foot. What are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $15,400?

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  1. perimeter = 2 x + 2 y

    cost = c = 14 x + 4 y = 15400
    or
    7 x + 2 y = 7700
    y = -3.5 x + 3850

    A = x y = x(-3.5 x + 3850)
    = -3.5 x^2 + 3850 x

    dA/dx = -7x +3850
    zero when
    x = 3850/7
    etc

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