D1 June 2009 Q5

EdexcelOld spec9 marksRoute Inspection

5.

Figure 3: network of paths with vertices A to H and lengths in m
Figure 3

[The total weight of the network is 625 m]

Figure 3 models a network of paths in a park. The number on each arc represents the length, in m, of that path.

Rob needs to travel along each path to inspect the surface. He wants to minimise the length of his route.

(a) Use the route inspection algorithm to find the length of his route. State the arcs that should be repeated. You should make your method and working clear. (6)

The surface on each path is to be renewed. A machine will be hired to do this task and driven along each path.

The machine will be delivered to point G and will start from there, but it may be collected from any point once the task is complete.

(b) Given that each path must be traversed at least once, determine the finishing point so that the length of the route is minimised. Give a reason for your answer and state the length of your route. (3)
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