One of the products Cleveland Trading keeps inventory of to sells to its customers is a pipe produced by Pittsburg Bros. PVC. Cleveland's weekly demand for these pipes is normally distributed with a mean of 573 pipes and standard deviation 155 pipes. The lead time for orders that Cleveland places with PBP for pipes is 10.6 weeks, and Cleveland uses a review period of 5 weeks.

a) Assume Cleveland uses an order-up-to level of 8,449 pipes. What will be the average on-hand inventory?

b) Again assume Cleveland uses an order-up-to level of 8,449 pipes. What will be the average pipe-line inventory?

c) Again assume Cleveland uses an order-up-to level of 8,449 pipes. How many stock-outs of pipes can they expect in a year?

d) How much on-hand inventory of pipes would Cleveland need to hold on average to bring the expected number of stock-outs per year down to 1? (Assume that lead time, review period and demand distribution remain the same.)