A high fashion label produces a designed women's dress for $100 a piece. The label does not have stores of their own, and sells through a dedicated retailer that runs boutique store in a prominent city. The demand during the fashion season is forecast by the label at 1000 units with a standard deviation of 200 units. The label wants to sell more units at list price, and offers the following buyback arrangement: The retailer buys the dress at $300 a piece from the label, and sells at a list price of $500 a piece. Any unsold inventory at the end of the fashion season is then purchased back by the label at a cost of $200 a piece and sold to third party or on-line outlets at a price of $150 a piece by the label. If the label wants the retailer to purchase at least 1200 items, what should be the minimum buy back price (recall it is currently at $200 a piece)