ZNKLO, a Japanese fashion brand/manufacturer, supplies seasonal fashion clothing items to Bossa Nova, a retailer in Santa Fe. When retailer orders from the manufacturer, the lead time is long, so the retailer is able to order only one time before the fashion season starts. At the end of the fashion season, any leftovers can only earn salvage price.

Consider a specific item for the coming season. The retailer purchases each unit of this item from the manufacturer for $75 and retails them for $115. The manufacturers production and shipping costs per unit are $35. At the end of the season, the retailer estimates that it will only be able to fetch $25 per leftover unit. The retailer believes this season's demand for this item can be represented by a normal distribution with a mean of 250 and a standard deviation of 125.

(a) What is the retailers optimal order quantity and its corresponding expected profit? What will be the manufacturers profit from selling to the retailer? (3 points)

Please clearly write all the inputs to the spreadsheet and the output that answers the question.

Retailers optimal order quantity:

Retailers optimal expected profit:

Manufacturers profit:

(b) If we take the total supply chain perspective and assume that the manufacturer and the retailer are combined into one integrated company, compute the optimal order quantity and expected profit for this combined company. (2 points)

Please clearly write all the inputs to the spreadsheet and the output that answers the question.

Optimal order quantity

Optimal expected profit