Could you solve it in detail

Question 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 $10, and the unit production cost is $5. The holding cost for each item not sold during the period is $6 (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 there are 0 elements in the inventory, there must be a production (producing 0 is not an option). If the demand exceeds the supply available 1 during the period, then those sales are lost and a shortage cost (including lost revenue) is incurred, namely, $9 and $21 for a shortage of 1 and 2 items, respectively. We want to determine the (long-run) expected average cost per period. Formulate this problem as an MDP and solve it via (a) Exhaustive enumeration, (b) LP formulation, (c) Policy iteration