Question 3 (Buy-Back Contracts) Zamatia Ltd. Is an Italian upscale maker of eyewear. UV inc., is one of their retailers in the United States. To match UV's stylish assortment, UV only operates small boutique stores located in trendy locations. Zamatia manufactures its sunglasses in Europe and Asia, so the replenishment lead time to the United States is long. Furthermore, the selling season is short and styles change significantly from year to year. As a result, UV receives only one delivery of Zamatia glasses before each season.

Consider Zamatia's sunglasses Prince being sold at the Manhattan boutique. UV purchases these sunglasses for $100 and retails them for $150. Zamatia's production and shipping costs per pair are $50. At the end of the season, UV generally needs to offer deep discounts to sell remaining inventory. UV estimates that it will only be able to fetch $30 per pair. The Manhattan store believes its demand for Prince is Normally distributed with mean 146 and standard deviation 43.

1) What is UV's optimal order quantity? 2) What is UV's profit? 3) What is Zamatia's profit?

Buy-back contract - Zamatia has now offered to buy back any unsold sunglasses for $60 at the end of the season. Assume Zamatia is able to obtain $30 per returned pair of glasses by selling them to a European outlet. The shipping cost for UV to send the sunglasses to Zamatia is estimated at $1.5 per pair.

4) What is UV's new order quantity? 5) What is UV's new profit? 6) What is Zamatia's new profit? Provide a qualitative explanation for the differences in profit between the two firms and two relationship types observed from your calculations in this exercise.