Edexcel FD2 AS 2022 June — Question 2

Exam BoardEdexcel
ModuleFD2 AS (Further Decision 2 AS)
Year2022
SessionJune
TopicNetwork Flows

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d7e250dc-9e38-4f65-a51a-c6a08082f310-03_1120_1757_212_153} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a capacitated, directed network of pipes. The number on each arc represents the capacity of the corresponding pipe. The numbers in circles represent a feasible flow from S to T.
  1. State the value of this flow.
  2. List the eight saturated arcs.
  3. Explain why arc EH can never be full to capacity.
  4. Find the capacity of
    1. cut \(C _ { 1 }\)
    2. cut \(C _ { 2 }\)
  5. Write down a flow-augmenting route that increases the flow by three units. Given that the flow through the network is increased by three units,
  6. prove that this new flow is maximal.