Hello, dcfi6052!
A rectangular field is going to be enclosed and divided into two separate rectangular areas.
Find the minimum fencing that is required if the total area of the field is 1200 mē.
First, make a sketch . . . Code:
: - - - - x - - - - :
*-------*-------------*
| | |
y| y| |y
| | |
*-------*-------------*
: - - - - x - - - - :
The area is 1200 mē: .$\displaystyle xy \,=\,1200\quad\Rightarrow\quad y \,= \,\frac{1200}{x}$ [1]
The total fencing is: .$\displaystyle F \:=\:2x + 3y$ [2]
Substitute [1] into [2]: .$\displaystyle F \:=\:2x + 3\left(\frac{1200}{x}\right)$
Therefore: .$\displaystyle F \;=\;2x + 3600x^{-1}$ is the function to be minimized.