Question: Due to slumping sales, Apple has decided to turn to revenue management to boost profits with the presale of their next line in smartphones, the iPhone. Apple plans to make 2.5 million of these phones available for sale. Some number of these phones will be available at the discount price of $100; however, phones at this price will be nonrefundable, no matter how frustrated a customer gets with the phone. They expect that they could sell all of the phones at this price. Customers who would like to be able to return the phone will pay the full price of $500. They expect the demand at this higher price to be normally distributed with a mean of 500,000 and standard deviation of 400,000.
What is the optimal protection level for the full priced iPhone?