Posted by **Henry** on Wednesday, April 10, 2013 at 1:40pm.

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 -
**Henry**, Wednesday, April 10, 2013 at 1:49pm
assume each pen encloses 200 square feet of area in the 2nd part sorry!

- Calculus Word Problem -
**Steve**, Wednesday, April 10, 2013 at 3:26pm
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)

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