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?
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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?