I am trying to prove that the min cut of the following network is 900. From looking at it I think it is obvious. I think the problem lies in the fact I have some infinite capacities and will need to prove that certain arcs are finite in capacity first. I am not sure how to do this in the most mathamatically correct way.
In the following graph, the green arcs have a maximum and minimum capacity equal to the value found on them. The remaining arcs and min,flow value and max. In that order. For example, it can be proved that the arc (S,ziA) has a min cut, and therefore a finite capacity, and then it can be proved that (s,z(i+1,A) has a min cut and a finite capacity. Then with these two facts it can be shown that the network has a min cut of 900. This proof seems messy to me. I wonder if I am missing something simpler enter image description here
I was unable to find any literature that could offer me a convention of how to proceed.
The arc from $w_{iA}$ to $z_{i+1,B}$ has a typo. Also, it is easy to find a feasible flow of value $1400$ (which turns out to be the maximum), so the minimum cut is at least $1400$ (which turns out to be the minimum).