# Calculus I Fencing Problem - Minimizing Dimensions with a Given Area

• Mar 8th 2009, 05:07 PM
essaymasters
Calculus I Fencing Problem - Minimizing Dimensions with a Given Area
Any help would be appreciated! The problem is as follows:
Quote:

An animal breeder wishes to create five adjacent rectangular pens, each with an area of 2400m^2. To ensure that the pens are large enough for grazing, the minimum for either dimension must be 10m. Find the dimensions required for the pens to keep the amount of fencing used to a minimum
• Mar 8th 2009, 05:26 PM
skeeter
Quote:

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

let $x$ = adjacent side lengths

$y$ = single pen widths

amount of fencing , $F = 6x + 10y$

$xy = 2400$

$y = \frac{2400}{x}$

sub $\frac{2400}{x}$ for y in the fence equation and minimize.
• Mar 8th 2009, 05:49 PM
essaymasters
Thank you!