Linear programming for X dimentions in web application (PHP) [closed]

I'm creating an engine for an application with optimization and I got stuck with it. First of all:

• There's a dynamic nummber of objects(Xi)
• There's a dynamic number of resources(Yj)
• I need to maximize the number of objects within the given resources

Speaking clearly: for example let's say we have a set resources i-->3 [10x1, 20x2, 30x3] and two objects j-->2 requiring features Y1[1x1, 3x2, 4x3] and Y2[0x1, 5x2, 2x3] and I want my program to - having the data(x1, x2, x3) - maximize the number of objects within given resources.

My question is - how do I encode it? I don't have problem with describing the mathematical formula, however I don't know how to make the computer calculate it. My program is written in PHP, which I feel comfortable in, so if it's possible I'd like to code it in PHP - but maybe there's a better option than that?