# Calculus Word Problem

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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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