5 The network shows the evacuation routes along corridors in a college, from two teaching areas to the exit, in case of a fire alarm sounding.\\
\includegraphics[max width=\textwidth, alt={}, center]{1aca4e91-d1b3-4a78-8880-e42a4fbf3ddb-14_729_1013_434_497}

The two teaching areas are at $A$ and $G$ and the exit is at $X$.

The number on each edge represents the maximum number of people that can travel along a particular corridor in one minute.
\begin{enumerate}[label=(\alph*)]
\item Find the value of the cut shown on the diagram.
\item Find the maximum flow along each of the routes $A B D X , G F B X$ and $G H E X$ and enter their values in the table on Figure 3 opposite.
\item \begin{enumerate}[label=(\roman*)]
\item Taking your answers to part (b) as the initial flow, use the labelling procedure on Figure 3 to find the maximum flow through the network. You should indicate any flow augmenting routes in the table and modify the potential increases and decreases of the flow on the network.
\item State the value of the maximum flow, and, on Figure 4, illustrate a possible flow along each edge corresponding to this maximum flow.
\end{enumerate}\item During one particular fire drill, there is an obstruction allowing no more than 45 people per minute to pass through vertex $B$. State the maximum number of people that can move through the network per minute during this fire drill.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 3}
  \includegraphics[alt={},max width=\textwidth]{1aca4e91-d1b3-4a78-8880-e42a4fbf3ddb-15_905_1559_331_292}
\end{center}
\end{figure}

Figure 4\\
\includegraphics[max width=\textwidth, alt={}, center]{1aca4e91-d1b3-4a78-8880-e42a4fbf3ddb-15_689_851_1370_598}

Maximum flow is $\_\_\_\_$ people per minute.
\end{enumerate}

\hfill \mbox{\textit{AQA D2 2011 Q5 [14]}}