3.
\begin{figure}[h]
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\caption{Figure 1
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[The total weight of the network is 451]}
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Figure 1 models a network of tracks in a forest that need to be inspected by a park ranger. The number on each arc is the length, in km, of that section of the forest track.
Each track must be traversed at least once and the length of the inspection route must be minimised. The inspection route taken by the ranger must start and end at vertex A.
- Use the route inspection algorithm to find the length of a shortest inspection route. State the arcs that should be repeated. You should make your method and working clear.
- State the number of times that vertex J would appear in the inspection route.
The landowner decides to build two huts, one hut at vertex K and the other hut at a different vertex. In future, the ranger will be able to start his inspection route at one hut and finish at the other. The inspection route must still traverse each track at least once.
- Determine where the other hut should be built so that the length of the route is minimised. You must give reasons for your answer and state a possible route and its length.