Saturday

October 25, 2014

October 25, 2014

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

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 11:12amL=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 - 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 ...

English/Argument - Statement: Five prominent Democratic senators support a new ...