# Such confusion

• Dec 2nd 2006, 08:02 PM
Tascja
Such confusion
An animal breeder wishes to create five adjacent rectangular pens, each with an area of 2400 m^2. To ensure that the pens are large enought for grazing, the minimum for either dimension must be 10 m. Find the dimensions of the pens in order to keep the amount used to a minimum.

How to i set up the 2 equations?? :confused:
• Dec 2nd 2006, 11:11 PM
earboth
Quote:

Originally Posted by Tascja
An animal breeder wishes to create five adjacent rectangular pens, each with an area of 2400 m^2. To ensure that the pens are large enought for grazing, the minimum for either dimension must be 10 m. Find the dimensions of the pens in order to keep the amount used to a minimum.

How to i set up the 2 equations?? :confused:

Hello Tascja,

in my opinion there is something missing here: "...the pens in order to keep the amountof something valuable/measurable used to a minimum..."
Therefore it isn't possible for me to set up the set of equations.

EB
• Dec 3rd 2006, 06:40 PM
Tascja
oo sorry.. was too tired .. i missed out: "...in order to keep that amount of fencing used to a minimum"
• Dec 3rd 2006, 07:20 PM
Soroban
Hello, Tascja!

Quote:

An animal breeder wishes to create five adjacent rectangular pens, each with an area of 2400 mē.
The minimum for either dimension must be 10 m.
Find the dimensions of the pens in order to minimize the amount of fencing.

Did you make a sketch?
Code:

: - - - - - - - - - x - - - - - - - - - :
*-------*-------*-------*-------*-------*
|      |      |      |      |      |
y|      y|      y|      |y      |y      |y
|      |      |      |      |      |
*-------*-------*-------*-------*-------*
: - - - - - - - - - x - - - - - - - - - :

Let $\displaystyle x$ = total length of all five pens.
Let $\displaystyle y$ = width of the pens.

We are told that the area is 2400 mē: .$\displaystyle xy \,=\,2400\quad\Rightarrow\quad y \,=\,\frac{2400}{x}$ [1]

The total fencing is: .$\displaystyle F \:=\:2x + 6y$ [2]

Substitute [1] into [2]: .$\displaystyle F\:=\:2x + 6\left(\frac{2400}{x}\right)\:=\:2x + 14,400x^{-1}$

And that is the function we must minimize.

. . Can you finish it now?

• Dec 3rd 2006, 07:26 PM
Tascja
still lost
But what about the height of each pen?? plus the questions says that each pen has an area of 2400 m^{2}... not that the whole thing has an area of 2400 m^{2}...
• Dec 3rd 2006, 08:05 PM
earboth
Quote:

Originally Posted by Tascja
But what about the height of each pen?? plus the questions says that each pen has an area of 2400 m^{2}... not that the whole thing has an area of 2400 m^{2}...

Hello Tascja,

replace the 2400 in Soroban's equation by $\displaystyle 5 \cdot 2400=12,000$.

That's all.

EB