2. The table shows the least distances, in km, between six towns, A, B, C, D, E and F.
| A | B | C | D | E | F |
| A | - | 16 | 25 | 21 | 12 | 15 |
| B | 16 | - | 24 | 22 | 21 | 12 |
| C | 25 | 24 | - | 18 | 30 | 27 |
| D | 21 | 22 | 18 | - | 15 | 12 |
| E | 12 | 21 | 30 | 15 | - | 18 |
| F | 15 | 12 | 27 | 12 | 18 | - |
Toby must visit each town at least once. He will start and finish at A and wishes to minimise the total distance.
- Use the nearest neighbour algorithm, starting at A , to find an upper bound for the length of Toby's route.
- Starting by deleting A, and all of its arcs, find a lower bound for the route length.