calculus help

Farmer Brown wants to fence in a rectangular plot in a large field, using a straight rock wall that is already there as the north boundary. The fencing for the east and west sides of the plot will cost $3 a yard, but she needs to use special fencing, which costs $5 a yard, on the south side of the plot. if the area of the plot is to be 600 square yards, find the dimensions of the plot that will minimize the cost of the fencing.

a) find the equation to maximized or minimized.

b) finding the solution.

c)showing that your solution is an absolute maximum or minimum.

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  1. length = 2 W + L

    area = W*L = 600 so L = 600/W

    C = 3(2W) + 5 L

    C = 6 W + 5(600/W) = 6 W +3000/W

    minimize C
    dC/dW = 0 = 6 - 3000/W^2

    W^2 = 3000/6 = 500

    W = 10 sqrt 5 = 22.36
    then L = 26.83

    is that max or min?
    d^2 C/d W^2 = 3000/W^4
    second derivative is always positive so curving up always, this is minimum cost

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