I Think you're looking at this the wrong way...
Three batches of beer a day is being an active brewery, not a yeast lab.
Yeast are grown in batches, not in a continuous way, especially if you mind consistency.
I suggest you start with one pack, split it to about 10 small starters, and build it up.
split each starter into 4 , and build each into a starter big enough for a batch.
that should be enough for brewing 3 beers a day * 14 days (assuming that's your primary length) . Now, after each batch finishes, wash the yeast cake and pitch all of it into one of tomorrows batches.
This doesn't require a lot of equipment, especially if you build the ~40 initial starters gradually, about one or two a day, so you could use under 20 containers for them.
This is how, to my understanding, breweries work.
You'll need a lot a mason jars, and make sure you label everything by date, type , and generation.
don't use yeast over a single digit generation...
You should develop a routine where you split some early starters into the next cycle's supply.
You probably should restart from a fresh pack every three months or so...