6. This question should be answered on the sheet provided.
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\caption{Fig. 3}
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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.
- Draw a complete network showing the shortest distances between the six areas.
(3 marks) - 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) - Improve this upper bound to find an upper bound of less than 55 miles.
- By deleting \(A\), find a lower bound for the total length of the route.