Optimization of slow mySQL queries on Amazon Web Services

We currently have an EC2 and RDS instance with Amazon Web Services. Our site is written in PHP, and the database is mySQL. We're running into slow queries on some pages and want to figure out alternatives to resolving the issues. The queries involve joins of two tables that have about 3 million records each, and a third table that has about 40,000 records. We've managed to improve our query time somewhat by experimenting with the queries, but it was still far too slow. We then tried experimenting with the parameter settings in RDS, but there wasn't any noticeable improvement, and in some cases it was worse. We're on a somewhat limited budget at the moment, and so upgrading our RDS instance is a last-resort option. However, if that's our only option at this point for marked improvement that still meets our business needs, we'd like to verify that as well. So, we're looking for someone who can help us with the following: 1) If possible at the outset, confirm whether our issues would require an upgrade of our instance or other fundamental platform changes to be improved. 2) Examine our queries to see if they can be optimized further 3) Examine our parameter group settings and recommend changes 4) If neither 2) or 3) resolve the issue, recommend changes to the data structure that could improve performance 5) Revisit question of fundamental platform changes We're also looking for someone who can advise us on how to avoid slowdown of the site while our product import is running, but ability to help with this part of the project will not be necessary in order to be awarded the contract. Because of the open-ended nature of this project, we would be paying by the hour, but we would have a cap on the number of hours spent on the project that could be extended by mutual agreement. The initial cap would be four hours of work. The data model will be provided once we have selected a contractor.