Interpreting Disequilibrium: Inelastic Supply and Demand at different quantities How does one go about interpreting a case of  inelastic supply and demand that are based at different quantities? There is no equilibrium in such a case and therefore nothing supplied or demanded. 

Two Questions
1.How would one go about looking at the the type of good we have here?2. Is this case even possible?
I am not sure what you mean by looking, but there is no equilibrium in this market, so any equilibrium analysis is impossible.
Situations like this are possible. Consider the Titanic. Supply of lifeboat spaces are limited and do not change depending on the price. People are willing to pay any price. 


There are limitations on what an individual can pay by money though. One might argue that there were a lot of people who were willing to do anything to get a space (push in line, etc.). As long as the number of these people is larger than the supply and the price is measured in effort your graph would describe the market for places.