Hello, Tascja!

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
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*-------*-------*-------*-------*-------*
: - - - - - - - - - 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?