I need to find a solution (all solutions, or at least upper and lower bounds) in positive integer numbers to the system $Ax \ge f$, where $A$ is an integer matrix.

With SageMath, I solved it with the function

Polyhedron.integral_points()

But, this is very slow and can take about 2-3 hours for a matrix which is about $30 \times 10$.

Is there another, faster way to do this? Preferably with SageMath or Python.