3 Mark is driving around the one-way system in Leicester. The following table shows the times, in minutes, for Mark to drive between four places: \(A , B , C\) and \(D\). Mark decides to start from \(A\), drive to the other three places and then return to \(A\).
Mark wants to keep his driving time to a minimum.
| \backslashbox{From}{To} | \(\boldsymbol { A }\) | \(\boldsymbol { B }\) | \(\boldsymbol { C }\) | \(\boldsymbol { D }\) |
| A | - | 8 | 6 | 11 |
| B | 14 | - | 13 | 25 |
| C | 14 | 9 | - | 17 |
| \(\boldsymbol { D }\) | 26 | 10 | 18 | - |
- Find the length of the tour \(A B C D A\).
- Find the length of the tour \(A D C B A\).
- Find the length of the tour using the nearest neighbour algorithm starting from \(A\).
- Write down which of your answers to parts (a), (b) and (c) gives the best upper bound for Mark's driving time.