Glenview Community College wants to build a rectangular parking lot on land bordered on one side by a highway. It has 380 feet of fencing to use on the other three sides. What should be the dimensions of the lot if the enclosed area is to be a maximum?

Answer 1

190 x 95 feet gives you the most area.
It gives you a 18,050 ft^2 area.
191 x 94.5 gives you 18,049.5 ft^2
189 x 95.5 gives you 18,049.5 ft^2

You can use calculus to get the result. The lot dimensions are L x 190 - L/2. L is the side parallel to the highway.
Area A = L*(190 - L/2) = 190L - L^2/2
dA/dL = 0 = 190 -L for a maximum
L = 190