# Mathematics

I am studying for my exams and do not know if I tackled correctly this word problem. Would appreciate any help. Thank you

"Tony and Doris wish to fence off part of their garden to create a
rectangular enclosure for their dogs. One side of the
enclosure will be provided by part of an existing wall. They have 220m of
fencing material available and wish to enclose as large an area as possible.
The length and width of the enclosure are denoted by l and w.

Question a): Write down an expression for the area A in terms of w and l. Also, write down an expression relating the length of the fencing to w and l.

Answer a): Area (A) = wl / Length of fencing (F) = 2w + l

Question b): Use the result from part (a) to write A in terms of w only.

Answer b):
F = 2w + l
220 = 2w + l
l = 220 - 2w
So A in terms of w is
A = wl
A = w(220 - 2w)
A = 220w - 2w^2

Question c): Use differentiation to determine the value of w that gives the maximum value for the area A enclosed and show that this is a local maximum. What is the maximum rectangular area that Tom and Barbara can enclose?

Answer c):
A = 220w - 2w^2
dA/dw = 220 - 4w

At a stationary point, we have
dA/dw = 0 = 220 - 4w
Solving for w gives, w = 55.
So the maximum area A achieved is when w = 55m.
Therefore, substituting w = 55 into the formula gives
F = 2w + l
220 = 2(55) + l
l = 110.
Hence the maximum rectangular area they can enclose is 55 * 110 = 6050m^2.

1. 👍 0
2. 👎 0
3. 👁 55
1. you are correct.

Just FYI to save time, maximum area is achieved when the fencing is divided equally among lengths and widths. So, 110 m are allocated to each group.
2 widths means w = 55
1 length means l = 110

1. 👍 1
2. 👎 0

## Similar Questions

1. ### Education Tech

1.) Which of the following is the best strategy for studying test? a) Sitting alone in a chair in a quiet room, looking over your textbook. b) Working in pairs and exchanging practice questions. c) Developing a personal method

asked by Ashley mccgarvey on January 9, 2014
2. ### riddles

what's the answer to this riddle. "There are 3 words in the English language that end in -gry.ONE is angry and the other is hungry. EVeryONE knows what the third ONE is means and what it stands for. EveryONE uses them everyday,

asked by Jasmin on June 20, 2007
3. ### English

The most important thing in life are making money, traveling aboard , and to live well. are begin used correctly I feel like the word should be replaced with the word is?

asked by Linda on May 19, 2015
4. ### L.A

The word aloof is an English word borrowed from Dutch. It's meaning is "at a distance". In which of the following sentences is the word used correctly? A. Anne's sociable nature made her aloof in new situations. B. When he first

asked by Dawn on April 14, 2015
5. ### Statistics

A survey among freshmen at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15. A sample of 36 students was selected.

asked by Anonymous on June 20, 2013
1. ### health crossword puzzle

studying about drugs i have a crossword puzzle and stuck need a 11 letter word that describes psychological depencene on a drug need a 11 letter word for : effect some drugs have when mixed together i got: sideaffects need 9

asked by marko on November 6, 2011
2. ### english

Rewrite the following sentence correctly using colons and/or semicolons. The semester was almost over consequently, many students were frantically studying.

asked by key on September 12, 2018
3. ### math

Claudia wants to test if the binomial 3x−6 is a factor of P(x)=3x3−9x2+9x−6. First, she evaluates P(_[blank 1]_). After simplifying correctly, she is left with a remainder of _[blank 2]_. Based on the remainder, she

asked by Auzy on December 10, 2019
4. ### Statistics/probability

Of 120 students, 60 are studying French, 50 are studying Latin and 20 are studying French and Latin. Find the probability that a student is: (a) studying French or Latin and (b) studying neither.

asked by Carline on March 19, 2009
5. ### English

I have a question its which diagram correctly represents this sentence? Sara, José, and Kenny were studying together for the test. How can I post a link to show you the diagrams?

asked by Emily on October 13, 2014
6. ### Grammar

How can i use the word cloy? i wrote this sentence but i'm not sure if i used the word correctly... "At first I thought you were appealing but now i realize that your just a cloy." I need help!! :D thanks in advance.

asked by Julie on July 15, 2010