# Optimization problem dealing with a fence and area.

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

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#### 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.

$2.19