Edexcel D1 — Question 6

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
TopicNetwork Flows

6. This question should be answered on the sheet provided in the answer booklet. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3147dad8-2d3c-42fd-b288-7017ff1fce16-003_469_844_422_1731} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} Figure 3 shows a capacitated, directed network. The number on each arc indicates the capacity of that arc.
  1. State the maximum flow along
    1. SAET,
    2. SBDT,
    3. SCFT.
      (3 marks)
  2. Show these maximum flows on Diagram 1 on the answer sheet.
    (1 mark)
  3. Taking your answer to part (b) as the initial flow pattern, use the labelling procedure to find a maximum flow from \(S\) to \(T\). Your working should be shown on Diagram 2. List each flow augmenting route you find, together with its flow.
    (6 marks)
  4. Indicate a maximum flow on Diagram 3.
    (2 marks)
  5. Prove that your flow is maximal.
    (2 marks)