Edexcel D2 2011 June — Question 5

Exam BoardEdexcel
ModuleD2 (Decision Mathematics 2)
Year2011
SessionJune
TopicNetwork Flows

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d28d78c1-052d-4350-a7e3-284380e3bbab-6_663_1363_242_351} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a capacitated directed network. The number on each arc is its capacity. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d28d78c1-052d-4350-a7e3-284380e3bbab-6_665_1363_1117_351} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows an initial flow through the same network.
  1. State the values of flows \(a , b\) and \(c\), and the value of the initial flow.
  2. By entering values along HG, HT and FG, complete the labelling procedure on Diagram 1 in the answer book.
  3. Find the maximum flow through the network. You must list each flow-augmenting route you use, together with its flow.
  4. State the value of the maximum flow through the network.
  5. Show your maximum flow on Diagram 2 in the answer book.
  6. Prove that your flow is maximal.