Problem: A long-distance telephone company uses a fiber optic network to transmit phone calls and other information between location. Calls are carried through cable lines and switching nodes. A portion of the company's transmission network is shown here. The numbers above each arc show the capacity in thousands of messages that can be transmitted over the branch of the network.
To keep with the volume of information transmitted between origin and destination points, use the network to determine the maximum number of messages that may be sent from a city located at node 1 to a city at node 7.