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A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area is to be 2484ft^2. The exterior fence costs $18.00 per foot and the interior fence costs $16.50 per foot. Find the dimensions of the pen that will minimize the cost. What is the minimum cost?

  • Calculus -

    if width=x, length=y, the cost=c, we have

    xy = 2484
    c = 16.50*2x + 18.00*(2x+2y)
    = 33x + 36x + 36(2484/x)
    = 69x + 89424/x

    dc/dx = 69 - 89424/x^2
    dc/dx=0 when x=36

    so, the cost is minimum when the pen is 36 by 69.

    I assume you can figure the cost.

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