A network of roads connecting towns in an alpine region is shown below.
The distances between neighbouring towns, represented by vertices, are given in kilometres.
The region receives a large snowfall, leaving all roads between the towns closed to traffic.
To ensure each town is accessible by car from every other town, some roads will be cleared.
The minimal total length of road, in kilometres, that needs to be cleared is
- 361 if `x` = 50 and `y` = 55
- 361 if `x` = 50 and `y` = 60
- 366 if `x` = 55 and `y` = 55
- 371 if `x` = 55 and `y` = 65
`text{A partial minimal spanning tree can be drawn:}`
`text{Consider each option:}`
`A:\ text{If} \ x=50 \ text{(include),} \ y = 55 \ text{(include)}`
`-> \ text{Total length} = 251 + 50 + 55 != 361 \ text{(incorrect)}`
`B:\ text{If} \ x=50 \ text{(include),} \ y = 60 \ text{(include)}`
`-> \ text{Total length} = 251 + 50 + 55 = 356 \ text{(correct)}`
`text{Similarly, options} \ C, D, E \ text{can be shown to be incorrect.}`
`=> B`
