SOLUTION: You have decided to become an alpaca farmer and need to make a rectangular pen for your animals to stay in. You have purchased 72 feet of fencing materials to make their pen, and y

Question 816302: You have decided to become an alpaca farmer and need to make a rectangular pen for your animals to stay in. You have purchased 72 feet of fencing materials to make their pen, and you would like to maximize the area of the pen so the alpaca can be as comfortable as possible.
A) Use what you know about the perimeter to determine the dimensions of the pen in terms of x.
http://imageshack.us/photo/my-images/543/896r.png/
B) Use Part A to write an equation to model the possible area of the pen in terms of x .
C) Use the equation you wrote in Part B to determine the maximum possible area of the alpaca pen.
D) An alpaca will feel comfortable in a pen with about 30 ft^2 per alpaca. How many alpacas can fit comfortably in the pen you created ?
Thanks for any help.

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
72 = 2L + 2w
a = Lw
L = a/w
---
72 = 2L + 2w
72 = 2a/w + 2w
2a/w + 2ww/w - 72 = 0
2a/w + 2ww/w - 72w/w = 0
2a + 2ww - 72w = 0w
2a = 0 - 2ww + 72w
a(w) = -(2/2)w^2 + (72/2)w
a(w) = -w^2 + 36w
---
the above quadratic equation is in standard form, with a=-1, b=36, and c=0
---
to solve the quadratic equation, plug this:
-1 36 0
into this: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic vertex is a maximum at: ( w= 18, a(w)= 324 )
---
Answer:
w = 18 ft
L = 18 ft
a(w)= 324 sq.ft
---
Number of alpacas that fit comfortably in the pen: 324/30 = 10 alpacas
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
RELATED QUESTIONS
I decide to take up alpaca farming. I will build an alpaca pan to my house. (since it is... (answered by ankor@dixie-net.com)

I decide to take up alpaca farming. I will build an alpaca pen next to my house. (Since... (answered by checkley77)

You Have 200 feet of fencing material to make a pen for livestock. If you make a... (answered by ewatrrr)

You have 200 feet of fencing material to make a pen for live stock. If you make a... (answered by htmentor)

A pen is to be formed by enclosing a rectangular fenced area in an open field. The pen... (answered by ikleyn)

A farmer has 60 m of wire fencing which he uses to make a rectangular pen for his sheep.... (answered by ikleyn)

I have been struggling to figure out this math problem and I was wondering if someone... (answered by scott8148)

You have 96 feet of fencing to enclose a rectangular pen for your dog. To provide... (answered by rfer)

Please help me answer: You have 120 feet of fencing to make a pen for your dog. You... (answered by mananth)