Continuing the previous problem, make the problem even more general by allowing upper bounds (arc capacities)

and lower bounds for the flows on the allowable arcs. Some of the upper bounds can be very large numbers, effectively indicating that there is no arc capacity for these arcs, and the lower bounds can be 0 or positive. If they are positive, then they indicate that some positive flow must occur on these arcs. Modify the model appropriately to handle these upper and lower bounds. You can make up the required bounds.