A hospital must order the drug Porapill from the manufacturer of the drug. It costs $500 to place an order. Annual demand for the drug is normally distributed with mean 10,000 and standard deviation 3000, and it costs $5 to hold one unit in inventory for one year. (A unit is a standard container for the drug.) Orders arrive one month after being placed. Assume that all shortages are backlogged.

a. What (R,Q) policy should the company use if it wants to meet 95% of all customer demand from existing inventory?

b. Suppose the company could pay C dollars per year to decrease its lead time per order from one month to half a month. What is the most it would be willing to pay to do this (and still have a 95% service level)?