Posted by **Anonymous** on Tuesday, October 25, 2011 at 2:48pm.

A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 100m^2. what are the dimensions of each pen that minimize the amount of fence that must be used?

- Calculus -
**Steve**, Tuesday, October 25, 2011 at 3:24pm
If each pen has width x and length y (against the barn),

the area is 4xy, and the fence used is 5x+8y

So, each pen has area 100.

p = 5x + 8(100/x) = 5x + 800/x

dp/dx = 5 - 800/x^2

dp/dx = 0 when x = √160 = 4√10

x = 4√10

y = 25/√10

- Calculus -
**Steve**, Tuesday, October 25, 2011 at 3:27pm
Now, if the barn is used as one wall of the pen, meaning only 3 sides have to be fenced, then

p = 5x+4y = 5x + 4(100/x) = 5x + 400/x

p' = 5 - 400/x^2

p' = 0 at x = 4√5

y = 25/√5

## Answer this Question

## Related Questions

- Calculus - A rancher plans to make four identical and adjacent rectangular pens ...
- College Algebra - A rancher needs to build four identical pens for his animals ...
- Math: pre calculus - a barn is 150 feet long and 75 feet wide. the owner has 240...
- Calculus Follow Up - A farmer wishes to build a fence for 6 adjacent rectangular...
- calculus - A dog kennel with four pens is to be constructed. The pens will be ...
- Calculus Word Problem - A farmer wishes to build a fence for 6 adjacent ...
- Calculus - A rancher wants to make a rectangular pen to house her animals. She ...
- Calculus 2 - A farmer wishes to build a fence for 6 adjacent rectangular pens. ...
- College Algebra and Trig - a rancher has 12,000 feet of fence to enclose 5 ...
- calculus - Farmer Jones has 210 meters of fence. She wishes to construct a ...

More Related Questions