A farmer owns k sheep. At the end of each year, a decision is made as to how many to sell or keep. The profit from selling a sheep in year i is pi. The sheep kept in year i will double in number in year i + 1. The farmer plans to sell out completely at the end of n years.

(a) Derive the general recursive equation for the problem.

(b) Solve the problem for n = 3 years, k = 2 sheep, p1 = $100, p2 = $130, and p3 = $120.