Jim wants to build a rectangular parking lot along a busy st

Jim wants to build a rectangular parking lot along a busy street but only has 1,800 feet of fencing available. If no fencing required along the street, find the maximum area of the parking lot. What is the maximum area of the parking lot? Square feet

Solution

Let x be the length and y be the width of parking lot

fence = 1800 feet

Permeter without street side length = x + y +y

x +2y = 1800 ----> x = 1800-2y

Area of parking lot = x*y = ( 1800-2y)y = 1800y -2y^2

Maximum Area occurs when dA/dy =0

So 1800 -4y =0

y = 1800/4 = 450 feet

x = 1800 -2*450 = 900

Maximum Area = 450*900 =405000 square feet