Instead, they had to feed them, house them, etc. It just doesn't seem to make sense from economic perspective to imprison people you were going to kill eventually.
Always more to say, but /u/estherke did a brief, clear writeup a few days ago on the organization of the camp system that should answer your questions.
EDIT: Also, from the FAQ, an answer to a similar question, by /u/coinsinmyrocket.
While there's always more that can be said, I strongly suggest you check out the extensive FAQ which has many posts on this.
But perhaps the best post on this topic is from /u/commiespaceinvader on Did economics motivate the Holocaust? The Nazi's had many economic motives involved, from slave labour to the confiscated possessions.