# Network flow - minimum flow through edge

In my max flow network, I would like to have an edge with upper bound of the flow (a.k.a. edge capacity) $$c_{max}$$. However, I would also like to add a lower bound for the flow through the edge, $$c_{min}$$.

I need to be sure that the minimum flow satisfies not only all the upper bounds (capacities), but also all the lower bounds.

Is it even possible? And if yes, which changes do I need to make to my flow network so that the max flow algorithm takes these lower bounds into account?