Okay... so it looks like, at bare minimum, 5 would get a production line going. If you could spare 8 though, I could skip the standalone finery forge and just build an ironworks.
That's:
> 4 for the iron works which contains the finery forge, or alternatively just 1 for a finery forge.
> 1 for the chandler
> 1 for slaughterhouse
> 1 for cooper's shop
> 1 for boiler
Salt pens don't take any luckily, and it looks like everything else can be purchased from NPCs on the markets.