Edexcel D1 2012 June — Question 4

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2012
SessionJune
TopicRoute Inspection

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4ad45e8f-f50a-4125-866b-a6951f85600f-5_661_1525_292_269} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} \section*{[The total weight of the network is 1436 m ]}
  1. Explain the term valency. Figure 3 models a system of underground pipes. The number on each arc represents the length, in metres, of that pipe. Pressure readings indicate that there is a leak in the system and an electronic device is to be used to inspect the system to locate the leak. The device will start and finish at A and travel along each pipe at least once. The length of this inspection route needs to be minimised.
  2. Use the route inspection algorithm to find the pipes that will need to be traversed twice. You should make your method and working clear.
  3. Find the length of the inspection route. Pipe HI is now found to be blocked; it is sealed and will not be replaced. An inspection route is now required that excludes pipe HI . The length of the inspection route must be minimised.
  4. Find the length of the minimum inspection route excluding HI. Justify your answer.
  5. Given that the device may now start at any vertex and finish at any vertex, find a minimum inspection route, excluding HI.