Application of Min Cost Flow to hostel bookings 
A hostel made a mistake concerning their bookings for 2017 and took many reservations without checking for free rooms in these periods.
  Every reservations is made for exactly one room and one period of time.
  All rooms are equal but were sold for different prices.
  The hostel now wants to cancel some bookings so everybody will have a room but at the same time the hostel wants to minimize its lost earnings. How would you solve the problem? Is it possible that no guest needs to change rooms during his stay?

I want to model the situation as a MinimumCostFlow-Problem. Where each vertex represents a day. We also add vertices s and t as the source and sink.
Edges between the verticees representing days should have infinite capacity and zero costs.
But I am still unfamiliar with the MinCostFlow-Problem and thus unsure how I need to set the flow constraints and other elements and appreciate any help.

I am unable to comment on Kuifje's answer, but hopefully the following is interesting. 
I agree with the modelling approach taken by Kuifje. In addition, to account for the limited room capacity, a further arc that connects the sink, $t$, to the source, $s$, can be added with a capacity equal to the number of available rooms. This assumes that the rooms are identical. When observing your final answer, paths through the "network" can be extracted manually to give individual room schedules.
Also, it should be sufficient to add a node for each booking instead of creating arcs. The example path from the comment on Kuifje's answer would be $s$ - $u$ - $v$ - $t$, where $u$ can connect to $v$ if the booking $v$ occurs after $u$ finishes. This gives the same result.
