6 The network shows the roads linking a warehouse at \(A\) and five shops, \(B , C , D , E\) and \(F\). The numbers on the edges show the lengths, in miles, of the roads. A delivery van leaves the warehouse, delivers to each of the shops and returns to the warehouse.
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1. Complete the table, on the page opposite, showing the shortest distances between the vertices.
2. 1. Find the total distance travelled if the van follows the cycle \(A E F B C D A\).
   2. Explain why your answer to part (b)(i) provides an upper bound for the minimum journey length.
3. Use the nearest neighbour algorithm starting from \(D\) to find a second upper bound.
4. By deleting \(A\), find a lower bound for the minimum journey length.
5. Given that the minimum journey length is \(T\), write down the best inequality for \(T\) that can be obtained from your answers to parts (b), (c) and (d).
   [0pt] [1 mark] \section*{Answer space for question 6} REFERENCE

6. 	\(\boldsymbol { A }\)	\(\boldsymbol { B }\)	\(\boldsymbol { C }\)	\(\boldsymbol { D }\)	\(\boldsymbol { E }\)	\(\boldsymbol { F }\)
   \(\boldsymbol { A }\)	-	7
   \(\boldsymbol { B }\)	7	-	5
   \(\boldsymbol { C }\)		5	-	4
   \(\boldsymbol { D }\)			4	-	6
   \(\boldsymbol { E }\)				6	-	10
   \(\boldsymbol { F }\)					10	-