Posted by **Michael** on Tuesday, March 27, 2012 at 9:28pm.

The Regional Farm Bureau (RFB) is preparing a brochure that offers advice about constructing pens for small farm animals, and they want us to be their consultants. They need us to carefully analyze the following situations and provide a detailed report. Then they will use our information to help them write the brochure.

In the example they wish to describe, it is assumed that the farmer has 900 feet of fencing with which to erect a rectangular pen alongside a long, existing fence (so the existing fence forms one side of the pen). Suppose the pen is to be subdivided into four parts in a two-by-two arrangement by including interior fences parallel to the outside boundaries. Then what dimensions make for the largest combined area? What if the farmer subdivides into nine pens in a three-by-three arrangement? What if the farmer subdivides into n2 pens in an n-by-n arrangement?

- Calculus -
**MathMate**, Wednesday, March 28, 2012 at 11:12am
L=length of fence available = 900 ft

For an nxn arrangement, with total dimensions x (parallel to existing fence) and y (perpendicular).

total area, A =xy

Total length of fence

=(n+1)y+nx=L

y=(L-nx)/(n+1)

A=xy

=x(L-nx)/(n+1)

For maximum area,

dA/dx=0

which gives

(L-2nx)/(n+1)=0

Solving for x,

x=L/2n

So total Area

A=xy

=x((L-nx)/(n+1)

=(L/2n)((L-n(L/2n))/(n+1)

=L^2/(4n(n+1))

## Answer this Question

## Related Questions

- Calculus - The Regional Farm Bureau (RFB) is preparing a brochure that offers ...
- math - A farmer has both chickens and sheep on his farm. He has a total of 25 ...
- math - In a farm the ratio of goats to cows is 3:4 if there are 420 farm animals...
- math - A farmer has $100.he has to buy 100 farm animals.He has to spend exactly...
- english - Of all of the characters in Animal Farm, are there any who seem to ...
- Animal Farm - Has anyone read the book Animal Farm by George Orwell? If so, they...
- Maths - A farm rears 9 ducks and cows in his farm. There are 28 legs altogether....
- Maths - A farm rears 9 ducks and cows in his farm. There are 28 legs altogether....
- Math - On joes farm there are 99 animals. There are four times as many cows as ...
- algebra - A farm raises a total of 220 chickens and pigs. The number of legs of ...