4 [Figures 4 and 5, printed on the insert, are provided for use in this question.]
The network shows the routes along corridors from the playgrounds \(A\) and \(G\) to the assembly hall in a school. The number on each edge represents the maximum number of pupils that can travel along the corridor in one minute.
\includegraphics[max width=\textwidth, alt={}, center]{587bccdf-abd7-4a08-a76e-61374f322e2e-04_1043_1573_559_228}

1. State the vertex that represents the assembly hall.
2. Find the value of the cut shown on the diagram.
3. State the maximum flow along the routes \(A B D\) and \(G E D\).
4. 1. Taking your answers to part (c) as the initial flow, use a labelling procedure on Figure 4 to find the maximum flow through the network.
   2. State the value of the maximum flow and, on Figure 5, illustrate a possible flow along each edge corresponding to this maximum flow.
   3. Verify that your flow is a maximum flow by finding a cut of the same value.
5. On a particular day, there is an obstruction allowing no more than 15 pupils per minute to pass through vertex \(E\). State the maximum number of pupils that can move through the network per minute on this particular day.