Edexcel D2 2015 June — Question 4

Exam BoardEdexcel
ModuleD2 (Decision Mathematics 2)
Year2015
SessionJune
TopicNetwork Flows

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{57c75bde-811a-421c-899a-3689bdba6724-5_837_1217_233_424} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a capacitated network. The capacity of each arc is shown on the arc. Two cuts \(\mathrm { C } _ { 1 }\) and \(\mathrm { C } _ { 2 }\) are shown.
  1. Find the capacity of each of the two cuts. Given that one of these two cuts is a minimum cut,
  2. write down the maximum possible flow through the network. Given that the network now has a maximal flow from S to T ,
  3. determine the flow along arc SB.
  4. Explain why arcs GF and GT cannot both be saturated. Given that arcs EC, AD and DF are saturated and that there is no flow along arc GF,
  5. determine a maximum flow pattern for this network and draw it on Diagram 1 in the answer book. You do not need to use the labelling procedure to determine the maximum flow.