2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{87f0e571-e708-4ca9-adc7-4ed18e144d32-03_716_1491_239_294}
\captionsetup{labelformat=empty}
\caption{Figure 3
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[The total weight of the network is 48.2]}
\end{figure}
A surveyor needs to check the state of a number of roads to see whether they need resurfacing. The roads that need to be checked are represented by the arcs in Figure 3. The number on each arc represents the length of that road in miles. To check all the roads, she needs to travel along each road at least once. She wishes to minimise the total distance travelled.
The surveyor's office is at F , so she starts and ends her journey at F .
- Find a route for the surveyor to follow. State your route and its length. You must make your method and reasoning clear.
The surveyor lives at D and wonders if she can reduce the distance travelled by starting from home and inspecting all the roads on the way to her office at F .
- By considering the pairings of all relevant nodes, find the arcs that will need to be traversed twice in the inspection route from D to F. You must make your method and working clear.
- Determine which of the two routes, the one starting at F and ending at F , or the one starting at D and ending at F , is longer. You must show your working.