NO NO NO NO NO
Do NOT go anywhere near the max tyre pressure! It will be around 55-60 psi, which if you inflate to that will leave you with a tiny grip patch with all the hazards that entails, along with wearing through the centre of the tread in no time!
Profile is not related to pressure. Sidewall flex is, as that's where you exert the loads on the tyre under cornering. Yes, lower profile tyre often have stiffer sidewalls and as such may require higher pressures, but tyre construction is far more important than profile size in determining pressure.