Virtually all the traffic exits at node $9$ to a manufacturing plant. On the link between any pair of nodes i and $j($intersections$)$ is a capacity $c_{ij}.$ This is the maximum flow in cars per hour on that link in the direction from $i$ to $j.$ An unknown amount of flow $A_1$ enters node $1,$ and an unknown amount of flow $A_2$ enters node $2.$ The sum of the flows. $A_1+A_2,$ exits to the factory at node $9.$ The flows are unknown because we are secking the maximum flow through the system. and motorists will divide themselves by experimentation into cars entering node $1$ and cars entering node $2.$ In general. motorists will not backtrack to gain advantage, and men will not ask for directions.

In the evening, flows reverse and leave the factory to cross the area and exit vis one of the two bridges. The flow capacitics on each link are different now, because traffic is generally facing downhill into the evening sun. Set up a math program or programs that will find the maximum flow through the svstem.