Newquay
570
890
680
680
−
K
890
630
Penzance
M
480
810
M
K
−
M
680
Saltash
630
M
M
570
890
M
−
K
Truro
680
480
410
K
630
680
K
−
a Use the nearest neighbour algorithm, starting from Truro, to find an upper bound for the minimum cost of travelling between the eight stations, starting and finishing at Truro.
PL E
The upper bounds found by using other stations as the start for nearest neighbour are: £48.90, £50.40, £49.60, £51.90, £52.70, £48.50.
b Which of these is the best upper bound?
c By considering the reduced network formed by removing Truro, find a lower bound for the minimum cost of travelling between the eight stations, starting and finishing at Truro. The lower bounds found by reducing the network by removing other stations are:
M
£44.50, £43.40, £44.00.
d Which of these is the best lower bound?
SA
e What can you deduce about the minimum cost of travelling between the eight stations, starting and finishing at Truro?
Original material © Cambridge University Press 2018