Selective pricing of technology products

Apple has recently launched the iPod nano under two different versions:2GB and 4GB. There are two types of
consumers of the iPod nano.Type 1 has relatively narrow musical tastes and can easily do with less than 500 songs.These consumers are willing to pay $200 for a 2GB or a 4GB.Type 2 consumers like to listen to many different songs.These consumers are willing to pay $220 for a 2GB
nano and $270 for a 4GB nano.Apple estimates that there are 20 million type 1 consumers and 15 million type 2 consumers.Ass me that it costs $50 to produce an iPod nano regardless of its capacity (2GB or 4GB).

(a) Suppose first that Apple were to sell only 4GB iPods (after all,they cost the same and some consumers prefer more than less). What is the optimal price for a 4GB iPod?What is the profit?

(b) Suppose now that both models are introduced on the market.What are the optimal prices for the two models (make sure to explain your reasoning very carefully). What is the profit? How is this pricing scheme called?Briefly discuss what is its purpose and why it could be useful.