8 The diagram below shows a network of pipes.
\includegraphics[max width=\textwidth, alt={}, center]{2e397d7b-b751-4f2c-aa0e-31dd4a071b56-08_764_1009_317_497}
The uncircled numbers on each arc represent the capacity of each pipe in \(\mathrm { m } ^ { 3 } \mathrm {~s} ^ { - 1 }\)
The circled numbers on each arc represent an initial feasible flow, in \(\mathrm { m } ^ { 3 } \mathrm {~s} ^ { - 1 }\), through the network.
The initial flow through pipe \(S D\) is \(x \mathrm {~m} ^ { 3 } \mathrm {~s} ^ { - 1 }\)
The initial flow through pipe \(D C\) is \(y \mathrm {~m} ^ { 3 } \mathrm {~s} ^ { - 1 }\)
The initial flow through pipe \(C B\) is \(\mathrm { z } ^ { 3 } \mathrm {~s} ^ { - 1 }\)
8
- By considering the flows at the source and the sink, explain why \(x = 7\)
8
| 8- Prove that the maximum flow through the network is at most \(27 \mathrm {~m} ^ { 3 } \mathrm {~s} ^ { - 1 }\)
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