Urgent: Inventory Model. Solve step by step.

Question:

Suppose you are the inventory manager of a Best Buy store. You are particularly interested in finding a good inventory policyfor 32" Sony Wega TV. Since the store is new, you rely on information that you obtained from other stores in the Greater Philadelphia area. Joe, the manager at Kings of Prussia says "Well buddy, I have the perfect inventory policy that I can tell you. I've been using it here for the last 5 years, and I haven't had a stock out. Then you obtain from him the following information:

Demand for Wega-32 TV follows a normal distribution with average annual demand of 120, and a standard deviation of 60. The lead time is one month, and the backorder penalty cost is $200. Joe follows a reorder point policy of 10 units and order one at a time

(a) Do you agree with Joe in terms of not losing one customer due to stockouts?

(b) Not satisfied with the fill rate achieved using the base stock policy, you decide that a (Q, r) model should provide better customer service at a lower inventory cost. Calculate the inventory policy that should be implemented to obtain a fill rate of 90%. The order cost is $35, the company use a holding cost rate of 10% per $/per year. The cost of a TV is $500. What is the backorder level, the inventory level, and the safety stock?