A train journey consists of a connected sequence of stages formed by edges on the directed network from Arlie to Bowen. The number of available seats for each stage is indicated beside the corresponding edge, as shown in the diagram. The five cuts, A, B, C, D and E, shown on the network, are attempts to find the maximum number of available seats that can be booked for a journey from Arlie to Bowen.

 

cut A Arlie cut B 4 cut C 0 3 1 9 4 7 cut D 8 Bowen 4 cut E