In Fallout: Shelter, managing the three available resources (Power, Food, Water) is an important mechanic. However, I'm not quite sure what determines the usage of these resources.
For food and water, I would expect it to be based on the amount of dwellers in the entire vault. However, it doesn't sound completely unreasonable that the function of some rooms may increase water usage.
What is food and water consumption based on?
Power ought to be tied to the production that goes on in the vault. But it isn't clear if empty rooms use power at the same rate as rooms being used (or at all). If so, the advice commonly given to not get too many dwellers too quickly could also hold true for rooms. Also, elevators may or may not use power.
How is power usage determined?
Best Answer
Just got a loading screen tip in the game (the wording may not be exactly the same, but the general meaning should):
This is certainly an official source, although not a very in-depth explanation. From this, one could draw the conclusion that rooms consume power regardless of occupancy, and only dwellers use water, even if this isn't explicitly stated.
To further investigate the details (unless some other source is available), I suppose someone will have to do some science.
Edit: It appears the good folks over at /r/foshelter/ have done quite a bit of science.
Some key points relating to the resource consumption (not absolute facts, but probably close to the truth):
There are a lot of other interesting points made in the thread linked above, so I really recommend checking it out. More detailed information is available here. If they keep the work up, this may be the go-to resource for data on the game.