5 The network below represents the streets in a small village. The weights on the arcs show distances in metres. The total length of all the streets shown is 2200 metres.
\includegraphics[max width=\textwidth, alt={}, center]{372c062a-793f-4fb8-a769-957479f5fce7-07_499_1264_367_402}

1. Apply Dijkstra's algorithm to the network, starting at \(A\), to find the shortest route from \(A\) to \(H\).
2. Write down the shortest route from \(A\) to \(E\) and the shortest route from \(A\) to \(G\). Sheng-Li needs to travel along every street to deliver leaflets. He will start and finish at \(A\).
3. Explain why Sheng-Li will need to repeat some streets.
4. Showing your working, find the length of the shortest route that Sheng-Li can take, starting and ending at \(A\), to deliver leaflets to every street. The streets have houses on both sides. Sheng-Li does not want to keep crossing the streets from one side to the other. His friend Nadia offers to help him. They decide that they will work together and set off from \(A\), with Sheng-Li delivering to one side of \(A B\) and Nadia delivering to the other side. Each street will have to be travelled along twice, either by both of them travelling along it once or by one of them travelling along it twice. Nadia and Sheng-Li travel \(A - B - C - E\). At this point Sheng-Li is called back to \(A\). He travels along \(E - C - A\), delivering leaflets on one side of \(C A\). Nadia completes the leaflet delivery on her own.
5. Calculate the minimum distance that Nadia will need to travel on her own to complete the delivery. Explain how your answer was achieved and how you know that it is the minimum possible distance.
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