[thargor90]

LPs can prove optimality of a result but sometimes this is to expensive and you stop as soon as you reach near optimality based on known bounds.

For several problems you can prove lower and/or upper bounds for the optimal results. For example you can prove that a route between two points may not be shorter than their distance.

If you use LP in production you often don't care about optimality and can work with suboptimal results very well. Worst case you stop after a timeout and just pick the best result.

Edit: I forgot to mention that during solving of a LP you usually get dynamically computed bounds. The branch and bounds algorithm works by computing bounds on relaxed problems that give upper bounds for the original problem.