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A company delivers parcels to houses in a village, using a van. The network below shows the roads in the village. Each node represents a road junction and the weight of each arc represents the length, in miles, of the road between the junctions.
\includegraphics[max width=\textwidth, alt={}, center]{8d4db82a-0daf-487a-a6eb-be3ce8e59141-08_1208_1193_502_407} The total length of all of the roads in the village is 31.4 miles. On one particular day, the driver is due to make deliveries to at least one house on each road, so the van must travel along each road at least once. However, the driver has forgotten to add fuel to the van and it only has 4.5 litres of fuel to use to make its deliveries. The van uses, on average, 1 litre of fuel to travel 7.8 miles along the roads of this village. Whilst making each delivery, the driver turns off the van's engine so it does not use any fuel. Determine whether the van has enough fuel for the driver to make all of the deliveries to houses on each road of the village, starting and finishing at the same junction. Fully justify your answer.
\includegraphics[max width=\textwidth, alt={}, center]{8d4db82a-0daf-487a-a6eb-be3ce8e59141-09_2489_1778_175_107}