I'll repost what I posted in the other thread first tick of age.. Should be all the info you need to know:

Caps are assuming non sage/mystic/rogue etc modifiers. though # of scientists will remain the same regardless of your race/pers.

Alchemy: Cap 30%, 1 prof=2% = 15 Profs to cap
Tools: Cap 20%, 1 prof=1% = 20 Profs to cap
Housing: Cap 15%, 1 prof=0.6% = 25 Profs to cap
Food: Cap 200%, 1 prof=10% = 20 Profs to cap
Military: Cap 15%, 1 prof=0.6%= 25 Profs to cap
Crime: Cap 100%, 1 prof=5% = 20 Profs to cap
Channeling: Cap 125%, 1 prof=6% = 21 Profs to cap

Total profs required to hit caps = 146