Let $N = (V, E)$ be a network in which the capacity of each edge is either $12$ or $18$.
Prove or disprove: The value of a maximum flow for $N$ can’t be $56$.
I'm trying to figure out how to definitely prove this. I think that this is not possible because of no combination of $12X + 18Y$ (where $X$ and $Y$ are integers) will ever $= 56$. Is there a better way of saying this? Am I right to say that an integer solution to $12X + 18Y = 56$ is what the Fold-Fulkerson algorithm implies?