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March 26, 2017

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A farmer wishes to build a fence for 6 adjacent rectangular pens. If there is 600 feet of fencing available, what are the dimensions of each pen that maximizes total pen area?
The image looks like this:

box box box
box box box

also:

If the interior fencing is $3.00 per foot and the perimeter is $5.00 per foot, what are the pen dimensions that minimize cost?

  • Calculus Word Problem - ,

    assume each pen encloses 200 square feet of area in the 2nd part sorry!

  • Calculus Word Problem - ,

    part 2:
    if each pen has width x and height y
    xy=200
    6x+8y=600
    you have no room to vary the dimensions. So, I assume the 600 feet of fencing does not apply to part 2. Accordingly,

    xy=200
    cost c = 5(3x+4y)+3(3x+4y)
    = 24x+32y
    = 24x+32(200/x)
    dc/dx = 24 - 6400/x^2
    = 8(3x^2-800)/x^2

    dc/dx = 0 when x = 20√(2/3)

    so, the pens are 20√(2/3) by 10√(3/2)

  • Calculus Word Problem - ,

    25'x25'

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