Waukesha, a small town in Wisconsin, is in the process of developing a road system for the downtown area. Bill Blackstone, a city planner, would like to determine the maximum number of cars that can flow through the town from west to east. The road network is shown in below figure. where the arcs represent the roads. The numbers by the nodes indicate the maximum number of cars (in hundreds of cars per hour) that can flow (or travel) from the various nodes. For example, the number 3 by node 1 (on the road from node 1 to node 2) indicates that 300 cars per hour can travel from node 1 to node 2. Likewise, the numbers 1, 1, and 2 by node 2 indicate that 100, 100, and 200 cars can travel per hour on the roads from node 2 to nodes 1, 4, and 6, respectively. 

Note that traffic can flow in both directions down a road. A zero (0) means no flow in that direction, or a one-way road. Unlike the transportation and assignment models, in which there are multiple origin nodes and multiple destination nodes, the typical maximal-flow model has a single starting node (origin) and a single ending node (destination).