What to expand the highly loaded site (Python, MySQL)?

There is a working site written on Python (Django), and the database - MySQL.
Since the developers did not work much on writing optimized code, the site tued out to be very difficult. And with a vision of tens of thousands a day, in the peak time, the server does not cope with the load and throws out those whom he did not have time to serve.
Here is a system of physical server:
1. 2 nuclei of 1,8GHZ ​​
2. RAM 2GB

That's what the server is deployed on now:
mysql + nginx + fastcgi

So the question : I would like to hear the opinion of experienced, or simply knowledgeable, which can be expanded. This site, so that it was as fast as possible, resourcely capacious? Or is this ligament the fastest? Maybe someone made a comparison of performance.
And it is also possible someone who knows how to optimize the server so that the gigan number of requests in the database does not lie down, maybe some kind of setting?
Thank you.