John is the manager at a grocery store. The average demand for a brand of cereal is 5 boxes per week. Each box costs $6. The replenishment lead time of the supplier is 3 weeks and the demand during that time has a Poisson distribution. It costs $20 to place a replenishment order and John has decided to place orders to guarantee a service level of 99% and incur an annual ordering cost of $400. Holding costs are based on a 20% annual rate and the cost a back order is $35 per unit-year. Assume 52 weeks/year.
a) What is the total inventory holding cost?
b) what is the total back order cost per year?
c) What is the safety stock?