Which are the odd-degree nodes? A
B
C
D
E
A
−
3
12
−
10
B
3
−
4
7
17
C
12
4
−
13
−
D
−
7
13
−
−
E
10
17
−
−
−
What is the least weight path connecting the odd nodes in the network in question 2?
4
Explain why the solution to the Chinese postman problem for the network in question 2 has total weight 73.
5
A groundsworker wants to use a line-painting machine to mark out a design on a pitch. The machine is faulty so once it has been switched off it cannot be switched on again. This means that some lines will be painted twice.
SA
M
The design is shown.
PL E
3
The small circle has radius 1 metre. It passes through the centre of the larger circle and touches the larger circle. The straight lines are diameters of the larger circle. Each metre uses 0.1 litres of paint.
a What is the minimum amount of paint that the groundsman needs? b Why, when the groundsman is pushing the machine, would he need to walk further than the distance travelled by the machine? c What else do you need to know to be able to calculate the minimum distance that the groundsman travels when marking out the lines?
6
The least weight route that uses every arc at least once is required for this network.
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