Consider a SC (one supplier and one retailer) distributing a very popular fashion product, which have a short selling season due to style changes from year to year. The retailer receives only one delivery from the supplier before each season. The retailer purchases the item for $55/unit and retails them for $95/unit. According to the past data, the demand distributes normally with a mean of 300 units and a standard deviation of 150 units per year. The suppliers production and shipping costs per unit are $25. At the end of the season, the retailer needs to offer discounts to sell remaining inventory at $20 per item.

(a) How many units should the retailer order?

(b) If the supplier offers an option to buy back from the retailer all leftover units for a full refund,

how many units should the retailer order? The shipping cost for the items sent back from

retailer to supplier is $2.50 per unit.

(c) What is the optimal buyback price that will maximize the SC surplus?