Question: Question 6: a) Determine the bicycle pathway that will require the minimum amount of construction to connect all the attractive areas of a park. Also show the total distance (arcs are measured in metres). (2 marks)

b) A large department store chain has stores in seven country areas. What route do you recommend for the driver of the delivery truck at the warehouse (represented by node 1) to take to each of the seven suburbs (represented by nodes 2 to 8)? The network of roads is shown in the diagram below (the diagram is not drawn to scale but the number on each road gives the road distances in kilometres between the junctions). Use a relevant process or algorithm to find the shortest route and state the distance. (2 marks)

c) The following network shows a telecommunications network connecting various trunk terminals to relay telephone calls. Equipment automatically routes a particular call over the first clear path found between the trunks connected to the respective telephones. The physical configuration of the system for determining how many calls can be made between any two connected trucks must be set in advance. How well a particular telephone system works can be quantified in terms of the maximum number of calls it can accommodate. Each call routed between two trunks can be treated as a flow. Determine the maximum flow that can be achieved for the network from the source at A to the sink at L by completing Table 1 below. (2 marks)