Optimize My Websites MySQL Application

General information for the website: Music and Lifestyle Publications
Kind of development: Customization of existing website
Description of requirements/features: I need some work done to optimize the MySQL application for both of my websites.

The problem is that both sites are exceeding MySQL query limit because of our growing visitor stats, when this happens, the website redirects to a wordpress install page and this lasts for close to an hour at a time.

Our web host says that the maximum number of database queries per user is 75,000/hr, and that unfortunately, it is not possible to increase this limit. So, I will need to modify the script such that it does not exceed the query limit.

They point me to http://www.sitepoint.com/article/optimizing-mysql-application to know on how to optimize MySQL usage of both websites.

The two websites we need this done for are www.wepluggoodmusic.com and www.conversationsabouther.net

I have attached a screenshot of the install page that each website start to redirect to when they have exceeded the MySQL limit.
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