yeah, so it'd require a massive amount of storage. but also, things like flour require base ingredients. do you think they'd have massive underground wheat fields? they'd probably have to be insanely large to support a population like that.
It really depends on the amount of time the Vault was designed to stay closed for. Assuming even the "Weaponized" Vaults of Fallout 3 were eventually supposed to open to the outside world, then most Vaults would have to have massive Hydroponics Bays. Vault 22 is a good example of how such a endeavor would be undertaken while being mass restrictive. (Though do keep in mind Scaling is in effect in these games. Vault 22's Hydroponics Facilities are far vaster then they appear within the game)
But again, it boils down to how long the Vault was slated to be sealed shut. For Vaults like Vault 8 - which were issued the All Clear Signal within a few Decades - their production facilities wouldn't need to be as expansive as Vault 101, which was designed to remain sealed permanently. Vault 13 is another good example in expansive hydroponics, since they were to remain sealed shut for two hundred years. Yet there are also Vaults like Bakersfield, which likely had
zero production facilities due to the fact the Vault was designed to fail.
As for a Luxury Vault were cost is no object...you could get away with a Cattle Yard and Fisheries, but they wouldn't be able to be maintained indefinitely. For starters, the inhabitants of such a Vault wouldn't dare do the agricultural work themselves, thus would rely on Protectrons and Robobrains. But also, just like the Dwellers themselves Fish and Cattle would run the risk of inbreeding after awhile. Faster for Fish and Cattle, given consumption rates.
It would actually be an interesting Failed Vault experience, really. A Luxury Vault where these people had gotten together and "stocked" it with all the necessities to maintain their lifestyles and the Robots needed to look after their investments, but no personal know-how of things like fixing said robots when they broke down, or how to maintain their luxurious food supply on their own. Or even adequate knowledge of how to effectively transplant these luxuries (Devote all this time and energy into building a winery, only to have the graqes wither and die on the vine).