Edexcel D2 2013 June — Question 3

Exam BoardEdexcel
ModuleD2 (Decision Mathematics 2)
Year2013
SessionJune
TopicNetwork Flows

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f3feef8a-32ba-4234-a5fa-cdd26ef6967d-4_778_1420_262_360} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a capacitated, directed network. The number on each arc represents the capacity of that arc. The numbers in circles represent an initial flow.
  1. State the value of the initial flow.
  2. State the capacity of cut \(\mathrm { C } _ { 1 }\). The labelling procedure has been used and the result drawn on Diagram 1 in the answer book.
  3. Use Diagram 1 to find the maximum flow through the network. You must list each flow-augmenting route you use, together with its flow.
    (4)
  4. Draw a maximum flow pattern on Diagram 2 in your answer book.
    (2)
  5. Prove that the flow shown in (d) is maximal.
    (2)