6 The network represents a railway system. The vertices represent the stations and the arcs represent the tracks. The weights on the arcs represent journey times between stations, in minutes. The sum of all the weights is 105 minutes.
\includegraphics[max width=\textwidth, alt={}, center]{8f17020a-14bf-4459-9241-1807b954a629-5_981_1215_468_477} Norah wants to travel around the system visiting every station. She wants to start and end at \(A\) and she wants to complete her journey in the shortest possible time.

1. Apply the nearest neighbour method starting at \(A\) to find two suitable tours and calculate the journey time for each of these tours. Which of these answers gives the better upper bound for Norah's journey time?
2. Construct a minimum spanning tree by using Prim's algorithm on the reduced network formed by deleting vertex \(G\) and all the arcs that are directly joined to \(G\). Draw a diagram to show the arcs in your tree. Hence calculate a lower bound for Norah's journey time. Norah now decides that she wants to use every section of track in her journey. She still wants to start and end at \(A\) and to complete her journey in the shortest possible time.
3. Calculate the journey time for Norah's new problem. Show your working; quickest times between stations may be found by inspection. State which arcs Norah will have to travel twice and how many times she will pass through station \(D\).