Solve all parts.

A farmer owns a total of k sheep. At the end of each year, a decision should be made as to how many to sell or keep. The profit of selling a sheep in year i is Pi. The sheep kept in year i will be doubled and tripled with 2/3 and 1/3 probabilities, respectively. The farmer plans to sell out all the sheep at the end of n years. Suppose that you want to formulate a probabilistic dynamic programming model that could be used to maximize the expected profit obtained from selling the sheep during n years. @ Identify the stage. (b) Write your state variable and decision variable at each stage. (c) Define the objective function fr(x) in terms of state variable x and stage t in words. : Write the last period's formulas explicitly. (e) . Write the recursive formula. (f ) Define your ultimate objective function