QQ-Mart is a local grocery store. It sells a certain type of cheese. Excess demand can be backordered. The monthly demand of the cheese follows a normal distribution with mean of 250 and variance of 225. QQ-Mart reviews its inventory continuously and will place order with size Q when the inventory level hits R.The fixed cost per ordering is $10. The unit purchase price is $5. The annual interest rate of 10% is used to estimate the holding cost.The lead time for purchasing the cheese from the manufacturer is one week. QQ-mart wants to achieve a service level target that no stock-out in 95% the cycles.(Assume there are four weeks in one month.)
1) What is the mean and variance of the demand in lead time?
2) What is Q and R such that the desired service level can be achieved?
3) What is the safety stock?