MARKOVIAN DECISION PROCESS- INFINITE MODEL

2) Consider an infinite-period inventory problem involving a single product where at the beginning of each period, a decision must be made about how many items to produce during that period. The setup cost is PhP100, and the unit production cost is PhP50. The holding cost of each item not sold during the period is PhP40 (a maximum of 2 items can be stored). The demand during each period has a known probability distribution, namely, a probability of 1/3 of 0, 1, and 2 items, respectively. If the demand exceeds the supply available during the period, then those sales are lost and a shortage cost (including lost revenue) is incurred, namely, PhP80 and PhP320 for a shortage of 1 and 2 items, respectively. a) Define and determine the States b) Define and determine the decisions c) Determine the cost matrix d) Identify the stationary policies and their corresponding transition matrix. e) Solve using the policy improvement algorithm to find the optimal policy