Model an inventory system for a single product as a Markov Chain. At the beginning of each period, a decision must be made about how many items to produce in 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 $4/unit. A maximum of two items can be stored. The demand during each period has a known probability distribution, namely, a probability of 1/3 for 0,1, or 2 units. When the demand exceeds the supply available during the period, those sales are lost. A shortage cost (including lost revenue) is incurred, namely $8 for a shortage of 1 unit and $32 for a shortage of 2 units. Consider a policy (R1) where 2 items are produced if no items are in inventory (State 0) at the beginning of a period. In contrast, no items are produced if there are any items in inventory. Let the states represent the inventory level at the beginning of the period. The transition matrix is given: 01201/31/31/312/31/3021/31/31/3 a. Identify the states and draw the transition diagram with probabilities. b. Determine the long-run expected average cost per period for this policy. Where 0=0.444, 1=0.333, and 2=0.233, c. Determine one other feasible production policy that management could propose that will not exceed two units in inventory. You do not need to determine the cost or transition diagram for this policy.