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# Optimization problem dealing with a fence and area.

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A farmer has 600 feet of fencing with which to enclose a rectangular plot. What is the maximum area he can enclose?

Hint: Find a model for the area of the rectangular plot and maximize by completing the square

https://brainmass.com/math/optimization/optimization-problem-determining-maximum-area-6168

#### Solution Preview

First let's find the function we want to maximize.
Le x and y be sides of a rectangular plot. We know that its perimeter has to be 600 feet.
So 2x+2y=600
=> x+y=600
=> ...

#### Solution Summary

The maximum area of a fenced enclosure is found by completing the square.

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