What is the number of PA's and IP's required to make it through different Cap levels from $40M up to $200M? No use of AAA allowed. I want to get an idea where the limit is for each before fatigue would become a factor.

I know this is a non-answer, but it greatly depends on quality of pitching and defense/range

Injuries off I assume...

PAs don't change across low to mid caps. You can squeeze by with 4800 to 5000 if you bat pitchers first. Otherwise ~5300-5500

i have used 1100 ip at $40M without an issue but my defense was great. At $80M, I think 1350 ip might be about right.

Keep in mind this all depends on the extent you can split you squad an allow a hand full of players to fatigue.