5.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-08_588_1428_230_322}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

[The total weight of the network is 166]

Figure 3 models a network of cycle lanes that must be inspected. The number on each arc represents the length, in km, of the corresponding cycle lane. Lance needs to cycle along each lane at least once and wishes to minimise the length of his inspection route.

He must start and finish at A.
\begin{enumerate}[label=(\alph*)]
\item Use an appropriate algorithm to find the length of the route. State the cycle lanes that Lance will need to traverse twice. You should make your method and working clear.\\
(6)
\item State the number of times that vertex C appears in Lance's route.\\
(1)

It is now decided that the inspection route may finish at any vertex. Lance will still start at A and must cycle along each lane at least once.
\item Determine the finishing point so that the length of the route is minimised. You must give reasons for your answer and state the length of this new minimum route.\\
(3)
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2021 Q5 [10]}}