Burger King has experienced huge success with its "Toy Story" promotion as a part of toys giveaway. However, it also had the problem of running out of stock in some restaurants and having a lot of leftover inventories in some others. Burger King has 200 restaurants whose toys are supplied by a distribution center. At the time the order must be placed with the factories in Asia, demand (units of toys) for the promotion at each restaurant is forecasted to be normal distributed with mean 2,251 and standard deviation 600. Suppose, six months in advance of the promotion, Burger King must make a single order for each restaurant. Furthermore, Burger King wants to have a service level (the in-stock probability) of 85%.
a. How many toys must each restaurant order?
b. How many customers (who want the toys) would not get the toys?
c. How many toys should Burger King expect to have at the end of the promotion?