AQA D1 2012 January — Question 4

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2012
SessionJanuary
TopicRoute Inspection

4 The following network shows the times, in minutes, taken by a policeman to walk along roads connecting 12 places, \(A , B , \ldots , L\), on his beat. Each day, the policeman has to walk along each road at least once, starting and finishing at \(A\).
\includegraphics[max width=\textwidth, alt={}, center]{5a414265-6273-41c5-ad5f-f6316bd774d0-08_1141_1313_461_360} The total of all the times in the network is 224 minutes.
  1. Find the length of an optimal Chinese postman route for the policeman.
  2. State the number of times that the vertex \(J\) would appear in a route corresponding to the length found in part (a).