How many doses does brewing potions create? I know there is a similar question floating around that dealt with poisons. I ask cause one potion dosage may differ depending of its use (alchemically, ingested, etc). Is a single brewing only a single application? Is there rule/s for a cost effective mass production? How do apothecaries make potions in bulk and make a viable profession with it?
A character creates a single dose of potion for every potion created.
There is no mention of doses at all in the magic item creation rules or potion creation rules, but each potion can only be used once, as they are Use Activated magic items:
Use Activated: This type of item simply has to be used in order to activate it. a character has to drink a potion, swing a sword, interpose a shield to deflect a blow in combat, look through a lens, sprinkle dust, wear a ring, or don a hat. Use activation is generally straightforward and self-explanatory.
And that can only be used once (from Potions):
A potion is a magic liquid that produces its effect when imbibed. Potions vary incredibly in appearance. Magic oils are similar to potions, except that oils are applied externally rather than imbibed. A potion or oil can be used only once. It can duplicate the effect of a spell of up to 3rd level that has a casting time of less than 1 minute and targets one or more creatures or objects.
This is evidenced by the Dilution Alchemy discovery for alchemists, which also allows them to increase their daily limit of doses created by one.
Once per day, the alchemist can dilute any one potion or elixir, creating two doses of the same potion from one.
However, it seems you have the wrong idea how profiting from magical item creation is supposed to work in Pathfinder, I suggest you take a look at the Crafting Magic Items for Profit topic.
A character is also allowed to create up to four potions in a single day (if they cost up to 250 gp), rather than the usual one magic item per day, usually limited to one day per 1000 gp limit.
Creating an item requires 8 hours of work per 1,000 gp in the item’s base price (or fraction thereof), with a minimum of at least 8 hours. Potions and scrolls are an exception to this rule; they can take as little as 2 hours to create (if their base price is 250 gp or less). Scrolls and potions whose base price is more than 250 gp, but less than 1,000 gp, take 8 hours to create, just like any other magic item.
Which means that creating potions is just as profitable as any other magic item.
Is there rule/s for a cost effective mass production? How do apothecaries make potions in bulk and make a viable profession with it?
The Pathfinder rule system adamantly does not model any kind of economics. There is absolutely no concept of supply, demand, or fluctuating prices with either. Even the barest scrutiny will find many instances of pure nonsense if you try to apply them rigorously. Breaking the in-game “economy” such as it is is trivially simple.
This is because there is no call for such modeling for the games that Pathfinder is designed to model. Prices and costs only exist for the purposes of deciding how easy or difficult various items are to use in an adventure—because Pathfinder is almost-solely about adventure. They are designed to be player-interfacing, while the actual economy of the game world operates through pure fiat hand-wave and the rules shown are just the facets of the economy that the players actually interact with. If you are looking for a game of deeper economic simulation, you either need to augment Pathfinder rules with something else, or use another system entirely. Pathfinder is not designed for such a game and cannot support one without rather significant changes and additions.
So your question on the whole is based off of a seriously-skewed premise that potion shops are run by the same rules that players see. They aren’t. They aren’t, in fact, run by any rules at all, barring some suggestions for the GM about market availability based on the size of the town. They instead run off of world-building: the potion shop exists, and has the stock that it does, because the GM (or module author) decided it would be there and have those potions, and for no other reason. And the players cannot do whatever it is the potion shop owner is doing because the players are adventurers and not potion shop owners, and Pathfinder doesn’t have rules for them to become potion shop owners. Pathfinder is not a game in which players can play potion shop owners running a potion shop: they can only play potion shop owners who have closed up shop to go on an adventure. (Even the seriously-flawed rules for investing in businesses are almost-purely about investment and not about actually running the shop and stocking it and so on.)
Armed with this understanding, the rest of your question is fairly simple to answer: the apparent answers that you doubted are no longer doubtful when you consider things in this manner.
First, the definition of “a potion” per the rules:
A potion is a magic liquid that produces its effect when imbibed. [...] A potion or oil can be used only once.
So “a potion” is specifically a single dose of this kind of liquid. Then we get to the potion-brewing rules:
Creating an item requires 8 hours of work per 1,000 gp in the item’s base price. [At minimum, potions] can take as little as 2 hours to create (if their base price is 250 gp or less).
So each “potion” takes a minimum of 2 hours. And a “potion” is defined as a single dose. So yes, you can create a maximum of four potions in a day. And no, potion shop owners may very well not be limited in the same fashion, but no, you can’t do whatever it is they are doing in a game of Pathfinder.