a rectangular field is going to be enclosed and divided into two separate rectangular areas.(The areas do not have to be equal.)Find the minimum fencing that is required if the total area of the field is 1200m2.:rolleyes:

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- Nov 28th 2006, 06:43 AMdcfi6052optimization problem(Find minimum fencing,given total area)
a rectangular field is going to be enclosed and divided into two separate rectangular areas.(The areas do not have to be equal.)Find the minimum fencing that is required if the total area of the field is 1200m2.:rolleyes:

- Nov 28th 2006, 08:06 AMCaptainBlack
- Nov 28th 2006, 08:14 AMdcfi6052
Yes, that is all of the information that is given.:(

- Nov 28th 2006, 09:22 AMSoroban
Hello, dcfi6052!

Quote:

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.

- Nov 28th 2006, 10:08 AMdcfi6052
Thx Soroban I appriciate the help.