D1 January 2011 Q5

EdexcelOld spec11 marksRoute Inspection

5.

Figure 5: network with arcs AB 2.5, AE 2.6, AC 3.2, BD 2.1, DE 1.9, DG 1.9, GI 2.0, EI 3.3, EF 3.2, CF 3.6, FH 3.5, HI 1.8
Figure 5

[The total weight of the network is 31.6 km]

Figure 5 models a network of roads. The road markings on these roads are to be renewed. The number on each arc represents the length, in km, of that road. In order to renew the road markings, each road must be traversed at least once.

(a) Use the route inspection algorithm, starting and finishing at A, to find a suitable route, which should be stated. You must make your method and working clear. (5)
(b) State the roads that must be traversed twice and the length of the route. (3)

The machine that will be used to renew the road markings can only be delivered to D. It will start at D, but it may finish at any vertex.
Each road must still be traversed at least once.

(c) Given that the route is to be minimised, determine where the machine should finish. Give reasons to justify your answer. (3)
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