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)

- Calculus Word Problem -
**Chris**, Wednesday, December 2, 2015 at 9:02am
25'x25'

## Answer This Question

## Related Questions

- Calculus Follow Up - A farmer wishes to build a fence for 6 adjacent rectangular...
- Calculus 2 - A farmer wishes to build a fence for 6 adjacent rectangular pens. ...
- Algebra - Word Problems: 1. A farmer has 2400 feet of fencing and wants to fence...
- math - a farmer has enough fencing to build 40 feet of fence. He wishes to build...
- Math please help - A farmer has 120 feet of fencing available to build a ...
- calculus - Farmer Jones has 210 meters of fence. She wishes to construct a ...
- Geometry - A farmer wants to fence in a rectangular pen using the wall of a barn...
- Calculus - Farmer Jones has 480 feet of fence. She wishes to construct a ...
- AP Calculus AB - A farmer wants to create a rectangular pen, which will be ...
- Math - Brenda is building a rectangular pen for her dog. She has enough fencing ...

More Related Questions