An independent demand purchased inventory items daily demand is normally distributed with a mean of 100 units and a standard deviation of 20 units per day. Its supply lead time is 5 days. This items fixed ordering cost is $20/order and its holding cost is $2.50/unit/year.

(a) Design an appropriate periodic review, order-up-to level inventory control policy for this item, such that the cycle service level is 72%. What is the resulting product fill rate? If there is a shortage cost of $5 per unit of shortage, compute the expected annual total relevant cost resulting from your policy.

(b) If a product fill rate of 95% is suggested, would you recommend adopting this service level policy? Explain