# Math Help - Such confusion

1. ## 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??

2. 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??
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

3. oo sorry.. was too tired .. i missed out: "...in order to keep that amount of fencing used to a minimum"

4. Hello, Tascja!

An animal breeder wishes to create five adjacent rectangular pens, each with an area of 2400 m².
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 $x$ = total length of all five pens.
Let $y$ = width of the pens.

We are told that the area is 2400 m²: . $xy \,=\,2400\quad\Rightarrow\quad y \,=\,\frac{2400}{x}$ [1]

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

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

And that is the function we must minimize.

. . Can you finish it now?

5. ## 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}...

6. 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 $5 \cdot 2400=12,000$.

That's all.

EB