AQA D1 2011 January — Question 5

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2011
SessionJanuary
TopicRoute Inspection

5 Norris delivers newspapers to houses on an estate. The network shows the streets on the estate. The number on each edge shows the length of the street, in metres. Norris starts from the newsagents located at vertex \(A\), and he must walk along all the streets at least once before returning to the newsagents.
\includegraphics[max width=\textwidth, alt={}, center]{d1e453d6-0abb-4a7e-87c1-28275074dd08-10_1045_931_552_557} The total length of the streets is 1215 metres.
  1. Give a reason why it is not possible to start at \(A\), walk along each street once only, and return to \(A\).
  2. Find the length of an optimal Chinese postman route around the estate, starting and finishing at \(A\).
  3. For an optimal Chinese postman route, state:
    1. the number of times that the vertex \(F\) would occur;
    2. the number of times that the vertex \(H\) would occur.
      \includegraphics[max width=\textwidth, alt={}]{d1e453d6-0abb-4a7e-87c1-28275074dd08-11_2486_1714_221_153}