How to solve Linear Programming problem with tighter Integer Programming constraints

I want to learn a bit about Linear Programming.

After some research, I decided to solve the Cutting Stock problem as an example to learn. After doing some more research, I feel like I finally understand Linear Programming enough to use a 3rd party solver to solve the problem. Yet, I've only found a suitable solver for non-integer solutions. Using this type of solver is it possible to solve the tighter integer constraints problem?

If so, can someone please post some resources that I can use to read and perhaps implement an integer solver using an existing solver.

My understanding of this topic is EXTREMELY low, and I'm simply looking to learn more about it, so if the problem as I have stated it doesn't make sense, please let me know.

Thanks.

This then guarantees (since the LP is a lower/upper bound on the IP) that the resulting integer solution is close to the optimal solution. One simple example of a rounding strategy for [0,1] variables is for a variable $x$ to toss a coin with probability of heads being $x$, and then set x to 1 if the coin returns heads. There are many more involved strategies for other problems as well. Best to google 'rounding LPs' or 'randomized rounding'