a 'minimum security prison' [=a prison in which prisoners are allowed more freedom than in most other prisons because they are not considered dangerous or likely to escape]
Ten years is the 'minimum' needed. = We'll need 10 years 'at a/the minimum'. [=we'll need at least 10 years]
We need to keep expenses 'to a (bare) minimum'. [=we need to keep expenses as low as possible]
(..) Agent Mulder, you're up. I'm sorry. Mulder... Good luck. I'd say this about exceeds your minimum daily requirement. Whoa! You've gotta train for that kind of heavy lifting. Poopy day? So... ...what do you do? (..)1998 The X Files