D1 June 2014 (R) Q4

EdexcelOld spec13 marksRoute Inspection

4.

Figure 4: weighted network with vertices A to I
Figure 4

[The total weight of the network is 359 cm]

Figure 4 represents the network of sensor wires used in a medical scanner. The number on each arc represents the length, in cm, of that section of wire.

After production, each scanner is tested.

A machine will be programmed to inspect each section of wire.

It will travel along each arc of the network at least once, starting and finishing at A. Its route must be of minimum length.

(a) Use the route inspection algorithm to find the length of a shortest inspection route. You must make your method and working clear. (5)

The machine will inspect 15 cm of wire per second.

(b) Calculate the total time taken, in seconds, to test 120 scanners. (2)

It is now possible for the machine to start at one vertex and finish at a different vertex. An inspection route of minimum length is still required.

(c) Explain why the machine should be programmed to start at a vertex with odd degree. (2)

Due to constraints at the factory, only B or D can be chosen as the starting point and there will also be a 2 second pause between tests.

(d) Determine the new minimum total time now taken to test 120 scanners. You must state which vertex you are starting from and make your calculations clear. (4)
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