D1 June 2010 Q4

EdexcelOld spec10 marksRoute Inspection

4.

Figure 2: network with arcs AB 5.6, AC 4.8, BE 8.3, BD 6.4, CD 7.6, CF 8.5, ED 4.3, EG 10.1, DG 8.5, FG 9.2
Figure 2

[The total weight of the network is 73.3 km]

Figure 2 models a network of tunnels that have to be inspected. The number on each arc represents the length, in km, of that tunnel.
Malcolm needs to travel through each tunnel at least once and wishes to minimise the length of his inspection route.
He must start and finish at A.

(a) Use the route inspection algorithm to find the tunnels that will need to be traversed twice. You should make your method and working clear. (5)
(b) Find a route of minimum length, starting and finishing at A.
State the length of your route. (3)

A new tunnel, CG, is under construction. It will be 10 km long.
Malcolm will have to include the new tunnel in his inspection route.

(c) What effect will the new tunnel have on the total length of his route?
Justify your answer. (2)
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