8
Figure 1 shows a network of water pipes.
The number on each arc represents the upper capacity for each pipe in litres per second.
The numbers in the circles represent an initial feasible flow of 103 litres per second.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{8d4db82a-0daf-487a-a6eb-be3ce8e59141-12_979_1074_589_466}
\end{figure}
8
- On Figure 1 above, add a supersource \(S\) and a supersink \(T\) to the network.
8
- Using flow augmentation, find the maximum flow through the network. You must indicate any flow augmenting paths clearly in the table below. You may use Figure 2, on the opposite page, in your solution.
| Augmenting Path | Extra Flow |
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| |
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\captionsetup{labelformat=empty}
\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{8d4db82a-0daf-487a-a6eb-be3ce8e59141-13_960_1074_315_466}
\end{figure}
8 - While the flow through the network is at its maximum value, the pipe EG develops a leak.
To repair the leak, an engineer turns off the flow of water through EG
The engineer claims that the maximum flow of water through the network will reduce by 31 litres per second.
Comment on the validity of the engineer's claim.