Phil sells Korean traditional items in a summer festival. The traditional hand-fan is one of his items. He purchased the hand-fans at #3,000 sells them in the festival at #5,000. Since the festival mark with date on the hand-fan, the value of the hand-fan will be only 500 after the festival ends. He can sell the leftovers in the local market. And he has to place the order a month before the festival. He estimates the probability distribution of the demand of the handfan. The organization of the festival will provide a local currency for traditional item sales. It means he can get 500 local currency for every sale of the hand-fan. 1. How many hand-fan Phil should order for the festival, to maximize his expected profit? 2. Now the seller of the hand-fan suggests a buy-back contract. According to the contract, the seller will buy back any leftover at 2000 . With the contract, What is the optimal service level and how many hand-fan Phil should order to maximize his expected profit? 3. (Extra Credit) If the estimated demand follows a normal distribution with mean 60 and standard deviation 12, how many hand-fan should Phil order?