4. The table shows the least distances, in km, between six towns \(A , B , C , D , E\) and \(F\).
| \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) |
| \(A\) | - | 98 | 123 | 68 | 96 | 71 |
| \(B\) | 98 | - | 74 | 129 | 47 | 120 |
| \(C\) | 123 | 74 | - | 102 | 111 | 63 |
| \(D\) | 68 | 129 | 102 | - | 85 | 59 |
| \(E\) | 96 | 47 | 111 | 85 | - | 115 |
| \(F\) | 71 | 120 | 63 | 59 | 115 | - |
- Starting at \(A\), and making your method clear, find an upper bound for the travelling salesman problem using the nearest neighbour algorithm.
- By deleting \(A\), and all of its arcs, find a lower bound for the travelling salesman problem.
- Write down an inequality about the length of the optimal route.