A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 132 feet of fencing, what is the largest area the farmer can enclose?
Let the width (perpendicular to the wall) of the rectangular area be X. There are two of these widths.
The length of the fence will then be 132 - 2X.
The area becomes: Area = X(132-2X).
It can be shown that this produces a maximum area when X = 33. (Use calculus; first derivative.)
Place this value back into the Area equation to find the area.