The owner of a lake must decide how many bass to catch and sell each year. If she sells x bass during year t, then a revenue r (x) is earned. The cost of catching x bass during a year is a function c(x,

b) of the number of bass caught during the year and of

b, the number of bass in the lake at the beginning of the year. Of course, bass do reproduce. To model this, we assume that the number of bass in the lake at the beginning of a year is 20% more than the number of bass left in the lake at the end of the previous year. Assume that there are 10,000 bass in the lake at the beginning of the first year. Develop a dynamic programming recursion that can be used to maximize the owner’s net profits over a T-year horizon.