Question: 5. (10) Consider an inventory system in which the sequence of events during each period is as follows. (1) We observe the inventory level (call

5. (10) Consider an inventory system in which the

5. (10) Consider an inventory system in which the sequence of events during each period is as follows. (1) We observe the inventory level (call it i ) at the beginning of the period. (2) If i1, 3i units are ordered. Otherwise, 0 units are ordered. Delivery of all ordered units is immediate. (3) With probability 1/4,0 unit is demanded during the period; with probability 1/4,1 unit is demanded during the period; and with probability 1/2,2 units are demanded during the period. (4) We observe the inventory at the beginning of the next period. Define a period's state to be the period's beginning inventory level. Give the transition probability matrix

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