18. Alien Auto Co. distributes parts for foreign cars in a large Midwestern city. Demand for a particular size of oil filter has been uniform. The lead time to obtain the filters is 1 month, and the average use rate is 500 per month. The lead-time use is normally distributed with a standard deviation of 70 units. Order cost is $12, and holding cost is $0.30 a year per filter. The estimated cost of a stockout is $10.

a. What is the EOQ?

b. How many orders per year will be placed at this EOQ?

c. What is the optimum probability of a stockout?

d. What is the optimum reorder level?

e. How much will Alien Auto spend per year to hold inventory on this filter if it implements the values you determined above?