# Math Help - optimization problem driving me crazy!

1. ## optimization problem driving me crazy!

The owner of a used tire store wants to construct a fence to enclose a rectangular outdoor storage area by using part of one side of the store, which is 110 feet long, as one of the sides of the enclosed area. There are 210 feet of fencing available for the other three sides of the enclosure. Find the dimensions of the outdoor enclosure with the most area.

so I know it is 2L+1w=210
A=L*w
w=210/2L
2L+(210/2L)=210
derive this? and set to zero? Thanks

2. Yes,

2l + w = 210

where $w \leq 110$

$A = l\times w$

So,

$w = 210 - 2l$

And $A = l(210-2l)$

Expand, find A' and set it to zero to get the maximum.

Solve for l to get the length of one side of the enclosure, then find w the length of the other side, making sure w satisfies the condition we set earlier.