# Optimization Word Problem Start Help

• Dec 17th 2009, 06:49 PM
StarlitxSunshine
Optimization Word Problem Start Help
A rectangular field is to be bounded by a fence on three sides and by a straight stream on the fourth side. Find the dimension of the field with maximum area that can be enclosed with 1000 feet of fence.

~I'm not really sure how to start with this question. I drew a rectangle surrounded by another rectangle, shaded outer side for the stream, but I'm not quite sure what to do next...

If you help me get started, that'd be great :)
• Dec 17th 2009, 06:52 PM
skeeter
Quote:

Originally Posted by StarlitxSunshine
A rectangular field is to be bounded by a fence on three sides and by a straight stream on the fourth side. Find the dimension of the field with maximum area that can be enclosed with 1000 feet of fence.

~I'm not really sure how to start with this question. I drew a rectangle surrounded by another rectangle, shaded outer side for the stream, but I'm not quite sure what to do next...

If you help me get started, that'd be great :)

let L = side parallel to the stream

W = sides perpendicular to the stream

2W+L = 1000

A = LW

get A in terms of a single variable, take the derivative and maximize.