# Thread: dimensions of a animal pen

1. ## dimensions of a animal pen

I tried using the second derivative and setting it equal to zero. Then plugging that number into 60 = LW (A = LW) to find the other side. I then put those numbers into the perimeter formula P = 3w + L. For some reason I keeping getting it wrong. What should I be doing instead?

A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal. The rectangular pen will have three wooden sides, which cost 20 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 50 dollars per foot to construct.
The animal requires an area of 60 square feet in order to be comfortable.

A) If the pen is to be built as cheaply as

possible, what are the dimensions of the pen that should be built?

L = ?

W = ?

B) How much will the pen cost to build?
$_________________ 2. Originally Posted by Babs0201 I tried using the second derivative and setting it equal to zero. Then plugging that number into 60 = LW (A = LW) to find the other side. I then put those numbers into the perimeter formula P = 3w + L. For some reason I keeping getting it wrong. What should I be doing instead? A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal. The rectangular pen will have three wooden sides, which cost 20 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 50 dollars per foot to construct. The animal requires an area of 60 square feet in order to be comfortable. A) If the pen is to be built as cheaply as possible, what are the dimensions of the pen that should be built? L = ? W = ? B) How much will the pen cost to build?$_________________
$\displaystyle xy=60$

and $\displaystyle P=2x+2y$

you are trying to minimize y

3. Originally Posted by Babs0201
I tried using the second derivative and setting it equal to zero. Then plugging that number into 60 = LW (A = LW) to find the other side. I then put those numbers into the perimeter formula P = 3w + L. For some reason I keeping getting it wrong. What should I be doing instead?

A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal. The rectangular pen will have three wooden sides, which cost 20 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 50 dollars per foot to construct.
The animal requires an area of 60 square feet in order to be comfortable.

A) If the pen is to be built as cheaply as

possible, what are the dimensions of the pen that should be built?

L = ?

W = ?

B) How much will the pen cost to build?
$_________________ First of all, the perimeter is$\displaystyle 2L + 2W$, but that isn't actually what you are interested in. We have that the cost (C) of three sides is$20 per foot, and one is $50 per foot:$\displaystyle C = 20L + 20W + 20L + 50W= 40L + 70W$. Now, given that$\displaystyle LW = 60$, we want to minimize$\displaystyle 40L + 70W$. So we substitute$\displaystyle L = \frac{60}{W}$and then we have that cost$\displaystyle C = \frac{2400}{W} + 70W$. Now all you have to do is minimize C in terms of W. 4. so I got$820, which was correct. Thank you!!!
so
w should = 6 ?
L should =10 ?

5. Originally Posted by Babs0201
so I got $820, which was correct. Thank you!!! so w should = 6 ? L should =10 ? I actually computed$\displaystyle W = \sqrt\frac{240}{7}\$, which is slightly less than 6.