Posted by **Catie** on Sunday, July 15, 2012 at 11:15pm.

A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area is to be 2484ft^2. The exterior fence costs $18.00 per foot and the interior fence costs $16.50 per foot. Find the dimensions of the pen that will minimize the cost. What is the minimum cost?

- Calculus -
**Steve**, Monday, July 16, 2012 at 10:36am
if width=x, length=y, the cost=c, we have

xy = 2484

c = 16.50*2x + 18.00*(2x+2y)

= 33x + 36x + 36(2484/x)

= 69x + 89424/x

dc/dx = 69 - 89424/x^2

dc/dx=0 when x=36

so, the cost is minimum when the pen is 36 by 69.

I assume you can figure the cost.

## Answer This Question

## Related Questions

- Calculus Follow Up - A farmer wishes to build a fence for 6 adjacent rectangular...
- Calculus Word Problem - A farmer wishes to build a fence for 6 adjacent ...
- Calculus - ABC Daycare wants to build a fence to enclose a rectangular ...
- calculus - A rectangular fence has to be built from both wood and metal so that ...
- Math - a 5 foot fence will be built around the perimeter of a 50 foot by 120 ...
- Calc - A farmer wishes to enclose a rectangular pen with area 100 square feet ...
- Calc - A farmer wishes to enclose a rectangular pen with area 100 square feet ...
- calc - A farmer wishes to enclose a rectangular pen with area 100 square feet ...
- MATH - A farmer wants to fence a small rectangular yard next to a barn. Fence ...
- Calculus - A fence is to be built to enclose a rectangular area of 310 square ...

More Related Questions