Max/Min flow of a network

Question

I have a network:

How do I figure out the maximum and minimum possible flow through each undefined branch?

Answer 1

Flow must meet the following criteria:

• Flow into a vertex must equal flow out
• Flow must be non-negative
• Flow must be less than or equal to capacity for each edge

For this, we'll have to assume the capacities are "$\infty$".

Vertex $A$ limits the flow of $f_1$ to 80, vertex $C$ limits it to 90. So we check if there is a flow through $f_1$ of 80: $f_1 = 80, f_2 = 0, f_3 = 10$ is a valid flow. We can also check if $0$ is a valid minimum: $f_1 = 0, f_2 = 80, f_3 = 90$.

Proceed similarly for $f_2$ and $f_3$. Just check "is there a valid flow with $f_n = x$?", you should be able to guess $x$ from the picture.