# Calculus

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!!!!!!!!!!

1. ๐ 0
2. ๐ 0
3. ๐ 66

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More Similar Questions
The text passage contains a mathematical question and its answer. The question is about a farmer who has 810 ft of fencing and wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. The goal is to find the largest possible total area of the four pens. The answer provided in the text is 16402.5 square feet, with the dimensions of the smaller rectangle being x=50.625 ft and y=81 ft.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Calculus

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!!!!!!!!!!

1. ๐ 0
2. ๐ 0
3. ๐ 66

## Similar Questions

1. ### math

a farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What is the largest area that can be enclose?

asked by kayla on October 26, 2008
2. ### calculus optimization problem

A farmer has 460 feet of fencing with which to enclose a rectangular grazing pen next to a barn. The farmer will use the barn as one side of the pen, and will use the fencing for the other three sides. find the dimension of the

asked by lori on March 30, 2013
3. ### Algebra

Farmer Ed has 9,000 meters ofโ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along theโ river, what is the largest area that can beโ enclosed?

asked by Janice on June 24, 2015
4. ### math

A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

asked by lulu on October 3, 2011
5. ### Math

A farmer with 8000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? Does that mean I have to

asked by muffy on September 12, 2009
6. ### intermediate algebra

A farmer with 3000 feet of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

asked by irma on March 8, 2010
7. ### Algebra 2

A farmer wants to enclose 2 adjacent rectangular regions next to a river. No fencing will be used next to the river. 60 meters of fencing will be used. What is the area of the largest region that can be enclosed. I need all of the

asked by Brandon on April 22, 2011
8. ### algebra

Farmer Ed has 9 comma 0009,000 meters ofโ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along theโ river, what is the largest area that can beโ enclosed?

asked by Janice on June 22, 2015
9. ### Applied Math- Gr.11

A farmer wants to enclose three sides of a rectangular pasture unsing 1000 yards of fencing. The fourth side does not require fencing because it borders a river. What dimensions (length and width) should the farmer choose in order

asked by Greg on May 1, 2008
10. ### Calc 1

A farmer with 700 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 area of the four pens?

asked by Grant on February 24, 2012

More Similar Questions
user
The text passage contains a mathematical question and its answer. The question is about a farmer who has 810 ft of fencing and wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. The goal is to find the largest possible total area of the four pens. The answer provided in the text is 16402.5 square feet, with the dimensions of the smaller rectangle being x=50.625 ft and y=81 ft.

TYPE: SINGLE_QUESTION_WITH_ANSWER