max pressure indicates the pressure at what the tire could suffer damage if used. Usually, when you transport tires that are already installed on rims, it´s safe to inflate them at max. pressure because it tends to get harder, thus, avoiding the risk of beeing deformated if someone puts any heavy weight on them for a long time (let's say someone has the brilliant idea of putting a heavy object for the 7 days the shipping time could take). Also, when your going out of town, leaving the car sitting still form more than 5 days, it's safe to inflate tires at max. pressure, to avoid deformation. However, that does not indicate by any mean that the tire SHOULD be used at that pressure, it's only a reference so you don't cause any damage to it. Usually 30 psi is more than enough for a 60 profile tire, between 32-38 for a 50 profile tire, and I think a 40 profile should need a little more like 38-46, but those numbres are from my personal experience (except the 40 profile which I have never used).