Most around here say they will hang two weeks if they have room, but during the busy season they are cut when they come around in the cooler, usually 7-10 days. I have only found one place that will hang 28 days. The USDA inspectors hate to see the hanging carcass turn green, but this one place is able to do it. Some places also determine hanging time by the fat cover, a carcass with a thin fat cover will dry out if hung too long.
Oops, I didn't read the question closely. The large commercial plants hang them for a short time. They use wet aging rather than dry aging.
Dry aging = hanging the carcass in the cooler.
Wet aging = storing the cut and boxed meat at just above freezing, this prevents mold while allowing breakdown.
A killing plant (most) is 24 hours or less. The one that I went to said it took 25 hours and 15 min from hoof to box. This being 1:15 process time with 24 hour hang time. They say the beef ages in the box.
Some cow and hog killing plants do what is call Hot debone. It is killed and deboned in a short period of time. It will go thought a blast chill before it is ground in to hamburger or sausage.
It is recommended to hang a carcass for 14 day. In college we had a professor that bought a side of beef, he wanted us to hang it till it fell off the rail and then hang it back up again for another 7 days. After 21 days there is to much triming that has to be done and a lot of loss.