20. Kick Up Your Heels shoe shop sells an average of 6 pairs of a particular brand of running shoe each week. The weekly demand for this item is normally distributed with a standard deviation of 2. The cost to process an order is $6, and the cost of holding a pair of these shoes in stock for a year is $8. In approximately 50 percent of the cases in which the shop is out of stock of this shoe and demand occurs, the sale will be lost because the customer decides to go to another store. The average profit on a sale of the shoe is $30 per pair. The lead time to obtain more shoes is 2 weeks.

a. Find the economic order quantity for the shoes.

b. Find the optimal probability of stockout during the lead time.

c. Find the optimal reorder level.