Let us consider six neighbouring towns A, B, C, D, E, and F. The distance k_{ij} between towns i and j (in miles) is indicated in Table 3.1 for towns that have roads connecting them. The population of the towns P_{i} is also given in the first row of Table 3.1.
Population (in thousands) 
3 
8 
2 
12 
7 
10 
A 
B 
C 
D 
E 
F 

A 
– 
50 
26 
– 
15 
32 
B 
50 
– 
– 
34 
28 
– 
C 
26 
– 
– 
29 
40 
17 
D 
– 
34 
29 
– 
18 
24 
E 
15 
28 
40 
18 
– 
43 
F 
32 
– 
17 
24 
43 
– 
A supermarket chain wishes to set up supermarkets at two towns such that the two supermarkets are accessible to the maximum number of people of the six neighbouring towns.^{1} Supermarkets are considered accessible if the distance ...
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