API / Server Optimisation to achieve max HTTP requests per second

We have a simple API in PHP that receives a geo-location as a HTTP Request and checks that location against others in a mysql database. If it finds one that matches, the response returned is a JSON string. We are using Apache Web Server and MySQL and at the moment on a VPS and also tested using Amazon AWS. Currently the amount of requests we are able to do per second is (approx 100) which is too low for what we want to achieve. We need to be able to get the requests as high as possible. 10,000 per second if able to or as close to it. As mentioned, this script is extremely simple and uses simple mathematics so no trig involved at the moment however we do have some upcoming functions that involve some trig calculations. Would like someone who has expertise in optimising either our code, web server config, mysql config or all of them to allow us to achieve these requests per second. We are sure that the number we are getting is ridiculously low considering our script is doing hardly anything. We will send through our script and sample DB to approved freelancer. Also open to offline discussion which is preferrable as we would obviously need to provide server specs. I am assuming this is only a few hours work however am prepared to pay high hourly rate for the result.