A farmer owns a herd of K sheep now. At the end of each year, the farmer decides how many to sell or keep. The profit from selling a sheep in year i is p_i. The sheep kept at the star of year i will double in size by the end of the year. The farmer plans to sell out completely at the end of n years.

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

(b) Specify the values in each stage assumed by the state and the alternative for n = 3 years as a function the initial herd size, K.