6 The network shows a system of pipes with the lower and upper capacities for each pipe in litres per minute.
\includegraphics[max width=\textwidth, alt={}, center]{c4dc61a7-47ee-4d5c-bf6d-30a5da2ee8dd-12_810_1433_429_306}

1. Find the value of the cut \(Q\).
2. Figure 3 opposite shows a partially completed diagram for a feasible flow of 24 litres per minute from \(S\) to \(T\). Indicate, on Figure 3, the flows along the edges \(B T , D E\) and \(E T\).
3. 1. Taking your answer from part (b) as an initial flow, indicate potential increases and decreases of the flow along each edge on Figure 4 opposite.
   2. Use flow augmentation on Figure 4 to find the maximum flow from \(S\) to \(T\). You should indicate any flow augmenting paths in the table and modify the potential increases and decreases of the flow on the network.
   3. Illustrate the maximum flow on Figure 5 opposite.
4. Find a cut with value equal to that of the maximum flow. You may wish to show the cut on the network above. \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{c4dc61a7-47ee-4d5c-bf6d-30a5da2ee8dd-13_759_1442_276_299}
   \end{figure} Figure 4 \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 5} \includegraphics[alt={},max width=\textwidth]{c4dc61a7-47ee-4d5c-bf6d-30a5da2ee8dd-13_764_1438_1930_296}
   \end{figure} \includegraphics[max width=\textwidth, alt={}, center]{c4dc61a7-47ee-4d5c-bf6d-30a5da2ee8dd-15_2349_1691_221_153}
   \includegraphics[max width=\textwidth, alt={}, center]{c4dc61a7-47ee-4d5c-bf6d-30a5da2ee8dd-16_2489_1719_221_150}