Homework Help: Calculus

Posted by Carla on Thursday, March 29, 2007 at 11:55pm.

Consider the following problem: A farmer with 810 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total are of the four pens?

your drawing should look like this

......................
. . . .
. . . .
. . . .
. . . .
. . . .
......................

then let the width of the smaller rectangle be x, let its length be y

so the amount of fencing would be
8x + 5y
so 8x+5y=810
y=(810-8x)/5

Area = 4xy = 4x(810-8x)/5
= 648x - 32x^2 /5

d(Area)/dx = 648 - (64/5)x = 0 for a max of Area
solve to get x=50.625
and subst to get y=81
for a max area of 4(50.625)(81)=16402.5

sorry, my diagram did not come out the way I hoped it would.
It is a large rectangle cut into four smaller ones.

Thank you!!!!!!!!!!

No one has answered this question yet.

Answer this Question

Related Questions

Calc 1 - A farmer with 700 ft of fencing wants to enclose a rectangular area and...
Calculus - A ostrich farmer wants to enclose a rectangular area and then divide ...
Calculus - A pig farmer wants to enclose a rectangular area and then divide it ...
Calculus - A cattle rancher wants to enclose a rectangular area and then divide ...
Algebra 2 - A farmer has 120 ft. of fencing available to enclose 2 adjacent ...
math - a farmer with 10,000 meters of fencing wants to enclose a rectangular ...
College Algebra - A farmer has 100 yeards of fencing with which to enclose two ...
Algebra - Math - A farmer has 100 yards of fencing with which to enclose two ...
Precalculus - You have a total of 820 feet of fencing to enclose a large ...
algebra - A farmer decides to enclose a rectangular garden, using the side of a ...

For Further Reading

First Name:
School Subject:
Answer: