5 Charlotte is visiting a city and plans to visit its five monuments: \(A , B , C , D\) and \(E\).
The network shows the time, in minutes, that a typical tourist would take to walk between the monuments on a busy weekday morning.
\includegraphics[max width=\textwidth, alt={}, center]{ba9e9840-ce27-4ca7-ab05-50461d135445-06_902_1134_529_543} Charlotte intends to walk from one monument to another until she has visited them all, before returning to her starting place. 5

1. Use the nearest neighbour algorithm, starting from \(A\), to find an upper bound for the minimum time for Charlotte's tour.
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2. By deleting vertex \(B\), find a lower bound for the minimum time for Charlotte's tour.
   [0pt] [3 marks]
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3. Charlotte wants to complete the tour in 52 minutes. Use your answers to parts (a) and (b) to comment on whether this could be possible.
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4. Charlotte takes 58 minutes to complete the tour. Evaluate your answers to part (a) and part (b) given this information.
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5. Explain how this model for a typical tourist's tour may not be applicable if the tourist walked between the monuments during the evening.