(a.) Suppose you have 500 feet of fencing to enclose a rectangular plot of land that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the maximum area?
(b.) A rectangular playground is fenced off and divided in two by another fence parallel to its width. If 900 feet of fencing is used, find the dimensions of the playground that will maximize the enclosed area. What is the maximum area?
(c.) A small car rental agency can rent every one of its 62 cars for $25 a day. For each $1 increase in rate, two fewer cars are rented. Find the rental amount that will maximize the agency's daily revenue. What is the maximum daily revenue?