Mickey Grocery Store specializes in gourmet sauces that are purchased from overseas. The purchasing cost of a special brand of sauce is $10 per jar and requires a 6month lead time. Mickey uses a 20% annual interest rate for computing holding costs and anticipates that penalty costs of not satisfying orders is $25 per jar. Ordering costs are about $50. During the replenishment lead time, the total demand is normally distributed with mean of 100 and standard deviation of 25.

a) Assuming that Mickey uses a Q,r type policy, estimate the optimal Q* and r* (rounding to the nearest integer).

b) Determine the annual costs of ordering, average inventory, and annual penalty costs.