AQA D1 2008 June — Question 5

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2008
SessionJune
TopicRoute Inspection

5 The diagram shows a network of sixteen roads on a housing estate. The number on each edge is the length, in metres, of the road. The total length of the sixteen roads is 1920 metres. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c5c963b-0183-4dc7-9054-b2c7a3eb8c1b-05_1371_1267_466_422} \captionsetup{labelformat=empty} \caption{Total Length = 1920 metres}
\end{figure}
  1. Chris, an ice-cream salesman, travels along each road at least once, starting and finishing at the point \(A\). Find the length of an optimal 'Chinese postman' route for Chris.
  2. Pascal, a paperboy, starts at \(A\) and walks along each road at least once before finishing at \(D\). Find the length of an optimal route for Pascal.
  3. Millie is to walk along all the roads at least once delivering leaflets. She can start her journey at any point and she can finish her journey at any point.
    1. Find the length of an optimal route for Millie.
    2. State the points from which Millie could start in order to achieve this optimal route.