6. This question should be answered on the sheet provided.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{4e50371b-0c1c-4b4e-b21d-60858ae160df-5_664_1029_335_440}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{center}
\end{figure}

The network in Figure 3 shows the distances, in miles, between a newspaper distributor based at area $A$, and five areas, $B , C , D , E$, and $F$, to which the distributor must deliver newspapers. Each morning a delivery van has to set out from $A$ and visit each of these areas before again returning to $A$, and the driver wishes to keep the total mileage to a minimum.
\begin{enumerate}[label=(\alph*)]
\item Draw a complete network showing the shortest distances between the six areas.\\
(3 marks)
\item Obtain a minimum spanning tree for the complete network and hence find an upper bound for the length of the driver's route.\\
(5 marks)
\item Improve this upper bound to find an upper bound of less than 55 miles.
\item By deleting $A$, find a lower bound for the total length of the route.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D2  Q6 [14]}}