Jim wants to build a rectangular parking lot along a busy street but only has 2,200 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot.

The perimeter of the parking:

2 W + L = 2,200 (there is no fence along the street)

L = 2200 - 2 W

The area of the parking is:

A = W x L = W (2,200 - 2 W) = 2,200 W - 2 W²

A' = 2,200 - 4 W

2,200 - 4 W = 0

4 W = 2,200

W = 2,200 : 4 = 550 ft

L = 2,200 - 1,100 = 1,100 ft

The maximum area is:

A max = 1,100 x 550 = 605,000 ft²