A hospital must order the drug Porapill from Daisy Drug Company. It costs $500 to place an order. Annual demand for the drug is normally distributed with mean 10,000 and standard deviation 3000, and...

A hospital must order the drug Porapill from Daisy Drug Company. 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 1 unit in inventory for 1 year. (A unit is a standard container for the drug.) Orders arrive 1 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 1 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)?