Zamatia Ltd. is an Italian upscale maker of eyewear. UV Inc. is one of their retailers in the US. Considering Zamatia’s entry-level sunglasses for the coming season, the Bassano UV purchases each one of those pairs of sunglasses from Zamatia for $75 and retails them for $115. Zamatia’s production and shipping costs per pair are $35. 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 $25 pe leftover Bassano. UV believes this seasons demand for Bassano can be represented by a normal distribution with a mean of 250 and a standard deviation of 125.

How many units of Bassano should UV order?

What order quanity would a firm choose if the firm owned both Zamatia and UV? I.e, what is the optimal order quantity to maximize the integrated supply chain’s profit?

Suppose Zamatia agrees to buy back from UV all leftover sunglasses for partial refund of $65 per pair. UV must ship leftover inventory back to Zamatia, which it estimates cost about $1.50 per pair. How many units should UV order to maximize its expected profit given the buy-back offer?