13.3 A farmer is considering the optimal course of action for his farm each year. The two options are to fertilize the farm and not to fertilize the farm. Optimality is defined such that the farmer will realize the highest expected revenue at the end of 4 years. The conditions (or states) of the farm are good (state 1), fair (state 2), and poor (state 3). If Pk and Rk (k 5 1, 2), which represent the transition probability matrix and the reward function matrix, respectively, are given by P1 5 0:2 0:5 0:3 0:0 0:5 0:5 0:0 0:0 1:0 2 4 3 5 R1 5 763 051 001 2 4 3 5 P2 5 0:2 0:6 0:1 0:1 0:6 0:3 0:1 0:4 0:5 2 4 3 5 R2 5 6 5 21 74 0 6 3 22 2 4 3 5 determine the optimal expected revenue and the optimal decision in each of the 4 years.