Plugins draining system resources

My site went down for a while yesterday. I'm hosted on a 2 cloud servers from Rackspace. One server for the database and a separate server for everything else. I submitted a support ticket to Rackspace when the site went down and got this message....

"The problem was, that there was a very large number of network connections to Apache that were hung in the CLOSE_WAIT state. I see that your server has been starving for RAM badly in recent memory (ie: using more RAM than it has), and Apache is getting killed for memory over-use frequently. To remedy this, I have reduced Apache's MaxClients setting to 10, which is more appropriate for your 1GB server, as your web-app is using as much as 100MB of RAM per connection. This is fairly high, and indicates that you probably have some plugin or other PHP code on your site that could use the attention of a web developer."

My question...how can I narrow down the plugin or plugins causing the problem? I need some advice for next steps and optimization. Right now the site only has 30 users, but there will be around 20,000 users in September.

Thanks, I look forward to your suggestions.