As far as Orc Production goes, you only need 2 Armories. But I am NOT protesting the extras, Armories are still most valuable for their military value. If anything, the only purposes Orc Breeding serves is to A) Make all the negotiators of the game have up to date Armories like everyone else and B) be a supply drain. But if you're already a good fighter and upgrade your Hero's Forge (once you get it, naturally) Orcs are last on your list of concerns.
I currently have 13 workshops.
Wow. I had two cities with only three workshops, only two of which were up to date. I will admit that that was on the low side, (very much so) but since I've definitely always gone on the lesser side for workshops that seems like a lot. Ahem. Anyway, I don't think supplies are such a MASSIVE concern to you with this kind of supply power, assuming you're on somewhat regularly, and you have PoP spells. If you have a Culture bonus above 125%, I can't imagine you in want of supplies.
But anyways, what I said still holds true. Stay above 10K Orcs, 20K if you're nearing your supply cap. But then start cranking out as many Orcs as you can when it's time to upgrade your small army of workshops.