2. (a) Explain the difference between the classical and the practical travelling salesperson problems. The table below shows the distances, in km, between six data collection points, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E }\), and F . Rachel must visit each collection point. She will start and finish at A and wishes to minimise the total distance travelled.
(b) Starting at A, use the nearest neighbour algorithm to obtain an upper bound. Make your method clear. Starting at B, a second upper bound of 293 km was found.
(c) State the better upper bound of these two, giving a reason for your answer. By deleting A, a lower bound was found to be 245 km .
(d) By deleting B, find a second lower bound. Make your method clear.
(e) State the better lower bound of these two, giving a reason for your answer.
(f) Taking your answers to (c) and (e), use inequalities to write down an interval that must contain the length of Rachel's optimal route.