I never did any linear/integer programming so I am wondering the following two things

- What are some efficient free linear programming solvers?
- What are some efficient commercial linear programming solvers?

It would be nice to supply a dummy usage example with each proposed answer.

Also what if wish to solve a integer programming problem? What are the answers to the above two questions in this case?

I know that integer LP is a hard problem but there are some relaxing methods that are sometimes employed in order to obtain a solution to an integer programming problem. Are there any software packages implementing this kind of stuff?