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An electronics store sells Christmas widgets made by Sony's widget division. It costs Sony $5 to make the widget. Sony will sell the widget to the electronics store at $10 and the store will sell the same widget to the customer at $18. If the widget is unsold at the end of the holiday season, it will have to be discarded. Assume that demand is normally distributed with a mean of 1000 with standard deviation of 200.

How many widgets should the retailer order? What are the expected profits for the retailer and Sony? What is the total profit of the supply chain?

Now consider a scenario where Sony will buy-back any unsold widgets from the retailer at the end of the season for $3. How many widgets should the retailer order? What are the expected profits for the retailer and Sony? What is the total profit of the supply chain?

Now consider a scenario where Sony will sell the widget to the retailer at cost ($5) but will take 48% of the sales revenue. How many widgets should the retailer order? What are the expected profits for the retailer and Sony? What is the total profit of the supply chain?