Loss-of-goodwill, backordering problem

Weekly demand for an on-line shoe retailer is approximately normally distributed with a mean of 12,000 and a standard deviation of 250 pairs of shoes per week. A pair of shoes costs $50 on average, and the retailer sells a pair of shoes for $85 on average. The retailer estimates the loss-of-goodwill cost to be $12/pair in case of a shortage and incurs an inventory holding cost of $10/pair/week.

a. How many pairs of shoes should this on-line retailer keep in stock at the beginning of each week if the customers are patient, i.e., are willing to backorder?

b. How many pairs of shoes should this on-line retailer have in stock at the beginning of each week, if the customers are impatient, i.e., are not willing to backorder and make the purchase from another on-line retailer?