First thing to check is your apache settings. (see
http://webwork.maa.org/wiki/Installation_Manual_for_2.13_on_Ubuntu_16.04#Configuring_Apache) I'm not sure if the live dvd already has these tweaked but in /etc/apache2/mods-available/mpm_prefork.conf, you should set:
MaxConnectionsPerChild 50
MaxRequestWorkers 30
These are only starting points. MaxConnectionsPerChild controls how many requests an apache process serves before it is killed off, and MaxRequestWorkers controls the maximum number of simultaneous apache processes that will answer requests. Generally 50 is a good value for the former. The latter will depend a bit on usage.
If you still have your old server running, you can also compare the values on it.
Another consideration is whether you are assigning gateway quizzes or just homework assignments. Quizzes are a lot harder on apache because they load all of the questions at once, whereas assignments will only load one question per page.