Help to Optimize drupal script or upgrade hosting?

One of my drupal sites is causing some problems:
1. 500 server problems where the page isn't displayed and other times it is displayed
2. pages that are there don't appear but go to my "page not found" page of drupal.
it seems that there is a Premature end of script headers on index.php
Asked my host about it and they tell me:
"Your account exceeds cpu/memory usage limits:
Sun Jan 22 17:59:02 2006: Script: '/home/mydomain/public_html/index.php', Domain: mydomain.com, Request: '/admin/help/system', Accessed from: -ip-number- - of mydomain using >16 MB Memory
You need to upgrade your account to higher package or optimize the scripts."
What can be done to optimize my drupal site instead of having to take a higher package?
Can anyone help?

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