A computer store sells hard disks purchased from a supplier, with a lead time of exactly 3 weeks. Weekly demand for hard disks has a normal distribution with mean 38 and variance 130. Each hard disk costs the store $18.80, and each order costs the store $75 in labor and materials. Holding costs are figured at 40% per year (a year is assumed to have 52 weeks). If the store cannot fill an order from on-hand inventory, it backorders it, and to attract customers, the store's sales policy is to give customers $400 in compensation per unsatisfied disk. The store is obliged by the supplier to purchase a lot of exactly 500 hard disks per order.

Answer the following questions:

4.1) Write down the model (policy) name and list all the parameters of the problem and their numerical values (rates should be per week).

4.2) Write down the name of the lead-time demand distribution, and compute its mean, ut, and its standard deviation, ot.

4.3) What are the numerical values of the optimal stocking policy? Include the formulas only for the policy parameter(s) you need to compute.

4.4) What is the safety stock level for this optimal policy?

4.5) What is the value of the Type 1 service level, a, of the optimal stocking policy?

4.6) What is the value of the Type 2 service level, b, of the optimal stocking policy?