The following graph represents bus routes between towns, and the weights are the costs of the journeys in dollars. A tourist staying at town A wishes to travel along all the routes and return to A as cheaply as possible. 5 H 3 6 B 4 5 6 5 6 E D 01 Find the minimum possible total cost. Q2 A new direct bus route is added between towns G and E. Explain why the addition of this route will result in a lower cost for travelling all the routes and write down the new amount. Task 4 The graph below shows the lengths of connecting roads in a factory complex. Each evening a security guard walks along all of the roads and returns to his office at vertex A. 40 10 50 30 30 B 60 60 80 80 60 60 C 40 20 30 30 D 30 9 50 H 40 50 EL 30 E 40 F 80 50 Q1 Find a route which minimizes the length of his walk and state its length. Q2 A friend offers to drop him off at one of the vertices and to pick him up at another. State which two vertices should be chosen to minimize the distance the security guard has to walk. Task 2 Q1 Explain why the following graph has an Eulerian trail but not an Eulerian circuit. A 13 12 B 17 C 14 16 23 23 12 D 14 6 G 16 F 14 E