Posted by **Marie** on Monday, April 23, 2012 at 7:45pm.

A cattle rancher wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). There are 480 feet of fencing available to complete the job. What is the largest possible total area of the six pens?

- Calculus -
**Damon**, Monday, April 23, 2012 at 8:17pm
finally I get to use calculus for this problem instead of completing square!

length total = 6 x

width = y

fencing = 7 y + 12 x = 480

so

y = (480-12x)/7

A = 6 x y

A = 6 (x)(480-12 x)/7

A = (6/7) (480 x - 12 x^2 )

dA/dx = (6/7)(480 - 24 x) = for max

24 x = 480

x = 20

then y = 240/7 = 34.3 approx

A = 6 x y = 6 * 20 * 240/7 = 4114.3

- Calculus -
**Damon**, Monday, April 23, 2012 at 8:19pm
I have done many of these fencing problems tonight but most were in algebra where I had to find the vertex of the parabola by completing the square instead of taking the derivative and setting it to zero. Using Calculus makes it much much easier.

## Answer This Question

## Related Questions

- calculus - A cattle rancher wants to enclose a rectangular area and then divide ...
- Calculus - A pig farmer wants to enclose a rectangular area and then divide it ...
- Maths - A rancher wants to enclose a rectangular area and then divide it into ...
- Calculus - A ostrich farmer wants to enclose a rectangular area and then divide ...
- Math - A pig farmer wants to enclose a rectangular area and then divide it into ...
- math - An ostrich farmer wants to enclose a rectangular area and then divide it ...
- Calc 1 - A farmer with 700 ft of fencing wants to enclose a rectangular area and...
- Calculus - Consider the following problem: A farmer with 810 ft of fencing wants...
- Precalculus - You have a total of 820 feet of fencing to enclose a large ...
- Calculus - Farmer Jones has 480 feet of fence. She wishes to construct a ...

More Related Questions