#4. Inventory chain. Electric store sells video game system and uses inventory policy that it keeps up to 5 units in stock in the store, and at the end of the day, they make a new order only if there are 0, 1 or 2 units left. The order comes over night, so the following day there are 5 units when the store opens. Let Xn = # units in stock at the end of the n-th day and Dn = demand in the n-th day, n E N. Assume Do's are i.i.d. with distribution given by the table k 0 1 | 2 | 3 | 4 | Dwi P(Da = k) 0.2 0.3 0.2 0.2 0.1 Suppose the store makes $20 profit on each unit sold, but it costs $3 a day to store a unit. (a) What is the long-run profit per day of this inventory policy? (b) If the store ends a day with 5 units in stock, what is the expected number of days until it closes again with 5 units in stock? (That is, what is the expected waiting time until first return to the state 5?) #4. Inventory chain. Electric store sells video game system and uses inventory policy that it keeps up to 5 units in stock in the store, and at the end of the day, they make a new order only if there are 0, 1 or 2 units left. The order comes over night, so the following day there are 5 units when the store opens. Let Xn = # units in stock at the end of the n-th day and Dn = demand in the n-th day, n E N. Assume Do's are i.i.d. with distribution given by the table k 0 1 | 2 | 3 | 4 | Dwi P(Da = k) 0.2 0.3 0.2 0.2 0.1 Suppose the store makes $20 profit on each unit sold, but it costs $3 a day to store a unit. (a) What is the long-run profit per day of this inventory policy? (b) If the store ends a day with 5 units in stock, what is the expected number of days until it closes again with 5 units in stock? (That is, what is the expected waiting time until first return to the state 5?)