| Exam Board | Edexcel |
| Module | D2 (Decision Mathematics 2) |
| Year | 2003 |
| Session | June |
| Topic | Travelling Salesman |
2. (a) Explain the difference between the classical and practical travelling salesman problems.
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The network in the diagram above shows the distances, in kilometres, between eight McBurger restaurants. An inspector from head office wishes to visit each restaurant. His route should start and finish at \(A\), visit each restaurant at least once and cover a minimum distance.
(b) Obtain a minimum spanning tree for the network using Kruskal's algorithm. You should draw your tree and state the order in which the arcs were added.
(c) Use your answer to part (b) to determine an initial upper bound for the length of the route.
(d) Starting from your initial upper bound and using an appropriate method, find an upper bound which is less than 135 km . State your tour.