6 Mia is on holiday in Venice. There are five places she wishes to visit: Rialto \(( R )\), St Mark's \(( S )\), Murano ( \(M\) ), Burano ( \(B\) ) and Lido ( \(L\) ). Boat services connect the five places. The table shows the times, in minutes, to travel between the places.
Mia wishes to keep her travelling time to a minimum.
| Rialto ( \(R\) ) | St Mark's ( \(S\) ) | Murano ( \(M\) ) | Burano (B) | Lido (L) |
| Rialto ( \(R\) ) | - | 15 | 55 | 75 | 25 |
| St Mark's ( \(S\) ) | 15 | - | 90 | 60 | 20 |
| Murano ( \(M\) ) | 55 | 90 | - | 25 | 80 |
| Burano (B) | 75 | 60 | 25 | - | 50 |
| Lido ( \(L\) ) | 25 | 20 | 80 | 50 | - |
- Find the length of the tour \(S R M B L S\).
- Find the length of the tour using the nearest neighbour algorithm starting from \(S\).
- By deleting Burano ( \(B\) ), find a lower bound for the length of the minimum tour.
- Sketch a network showing the edges that give the lower bound found in part (b) and comment on its significance.