Are there any real life case studies of someone building an MVP and shaping their product based on feedback and eventually becoming profitable?

Are you looking for a pdf, telling you about this process in an individual company? It seems like you are describing what all new companies go through.

Have you read Eric Ries' Lean Startup? The book is a collection of case studies of MVPs with feedback loops built in, and also case studies of what happens when you don't do that...

Dropbox ?

Did you read "Running Lean" ?