# optimization problem

• Mar 25th 2010, 02:33 PM
nuclear123
optimization problem
question:
find the length and width of a rectangle that has the given perimter and a maximum area

data given:
perimeter = 80meters

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any help?
2l+2w=80 <--- put in terms of either variable???

i got [80-2w/2] = Length

and i plugged this into the equation for the area of a rectangle...

Area = L*W
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area = [80-2w/2] * W

then i differentiate area = [80-2w/2] * W and find the critical numbers and get the maximum.....am i doing this correct lol?
• Mar 25th 2010, 02:58 PM
skeeter
Quote:

Originally Posted by nuclear123

area = [(80-2w)/2] * W

yes ... it might make things easier if you simplify as you go along.

$A = (40-w)w$