You are selling a software product called $$Link$$ which is available in high and low$-$quality versions called Link Professional and Link Home respectively. You have $2$ units of Link Professional and $2$ units of Link Home.

There are $2$ potential customers, each of whom is interested in buying $1$ unit of Link $($either Link Professional or Home but not both$).$ Suppose that your objective is to maximize the total revenue from selling the software. Further, you do not know the identity of either buyer and you must sell by posting one price for Link Professional and another price for Link Home. Each buyer seeks to maximize her consumer surplus and may buy Link Professional or Link Home or neither depending on the prices that you post. Please show all the intermediate steps and clearly explain your reasoning.

What is the optimal price and resulting revenue under the following scenario? What $($if anything$)$ would each customer buy?

If you could identify each buyer and make targeted offers, what price would you offer to each and how much revenue would you earn? What $($if anything$)$ would each customer buy?