A small warehouse has extra space wants to rent storage cages made out of fencing. To make the cages the warehouse manager wants to use 500ft of fencing material to enclose a large rectangle and then divide it into 20 cages with fencing parallel to one side of the rectangle. Since the cages will be rented at $10 per ft2 use calculus to find the dimensions of the an individual cage that maximizes area and the maximum total income that all the cages will produce.