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 $200.$

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?

Parts $1$ and $2$ are correct. Part $3$ is wrong. Look at the formulas for Cu$,$ Co and optimal profit.