6 [Figures 4 and 5, printed on the insert, are provided for use in this question.]
The network shows the routes along corridors from two arrival gates to the passport control area, \(P\), in a small airport. The number on each edge represents the maximum number of passengers that can travel along a particular corridor in one minute.
\includegraphics[max width=\textwidth, alt={}, center]{6c407dbf-efe5-49e4-881f-91e7de5c46d9-7_933_1063_552_486}

1. State the vertices that represent the arrival gates.
2. Find the value of the cut shown on the network.
3. State the maximum flow along each of the routes UTSP and RQVP.
4. 1. Taking your answers to part (c) as the initial flow, use the labelling procedure on Figure 4 to find the maximum flow through the network. You should indicate any flow augmenting paths in the table and modify the potential increases and decreases of the flow on 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.
5. On a particular day, there is an obstruction allowing no more than 50 passengers per minute to pass through vertex \(V\). State the maximum number of passengers that can move through the network per minute on this particular day.
   (2 marks)