Edexcel D2 — Question 8

Exam BoardEdexcel
ModuleD2 (Decision Mathematics 2)
TopicNetwork Flows

8. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 4} \includegraphics[alt={},max width=\textwidth]{195b1c1f-5ce3-4762-80c3-34c26382b88b-008_521_1404_285_343}
\end{figure} The network in Fig. 4 models a drainage system. The number on each arc indicates the capacity of that arc, in litres per second.
  1. Write down the source vertices. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 5} \includegraphics[alt={},max width=\textwidth]{195b1c1f-5ce3-4762-80c3-34c26382b88b-008_521_1402_1170_343}
    \end{figure} Figure 5 shows a feasible flow through the same network.
  2. State the value of the feasible flow shown in Fig. 5. Taking the flow in Fig. 5 as your initial flow pattern,
  3. use the labelling procedure on Diagram 1 to find a maximum flow through this network. You should list each flow-augmenting route you use, together with its flow.
  4. Show the maximal flow on Diagram 2 and state its value.
  5. Prove that your flow is maximal.