Step 1: Formulate the model as an MDP (Markov Decision Process) - States: The system has four states, {s1, s2, s3, s4}. - Actions: At each state, the decision maker has two possible actions: 'leave' the system and receive a reward of R = 20 units, or 'remain' in the system and receive a reward of r(si) = i units for state si. - Transition probabilities: The transition probabilities are given by the matrix P. - Rewards: The immediate reward for remaining is r(si) = i, and the reward for leaving is R = 20. - Discount factor: The discount rate is given as 0.9. Step 2/7 Step 2: Define the decision epochs and rewards - Decision epochs occur at each discrete time step. - The reward function is defined as follows: - If the action is 'remain', the reward is r(si) = i for state si. - If the action is 'leave', the reward is R = 20, regardless of the state. Step 3/7 Step 3: Use policy iteration to find the optimal policy - Initialize a random policy, for example, always 'remain'. - Evaluate the policy by solving the system of linear equations to find the value function