E$-$mail messages sent over the Internet are broken up into electronic packets

that may take a variety of different paths to reach their destination where the

original message is reassembled. Suppose the nodes in the graph shown in

Figure $5\mathrm{.}42$ represents a series of computer hubs on the Internet and the arcs

represent connections between them. Suppose the values on the arcs represent

the number of packets per minute $($in $1,000,000$s$)$ that can be transmitted over

each arc.a$.$ Implement a network flow model to determine the maximum number of packets

that can flow from node $1$ to node $12$ in $1$ minute.

b$.$ What is the maximum flow?