At least make sure you have a fairly modern machine (dedicated, not shared) of round 2GHz, a 100MHz link to the net instead of 10MHz and have Nginx/php-fpm instead of Apache webserver installed. This should take you a long way to your minimum requirements. If this does not do the trick you probably have to cluster or cloud several machines. Clustering is more barebones to the machine but harder to install and finetune/maintain. Clouding is to install virtual machine software which is easier but somewhat costlier with resources.

Also check your SQL, often a lot of cpu cycles are wasted on shoddy database interaction.