Question 2 MLC is organising a fun-run around this circuit. There are many activities that need to be completed for the fun-run to operate smoothly. These activities, with their immediate predecessors, are listed in the table below. Activity Predecessor(s) B S D E F G Time (minutes) 30 30 30 30 30 60 180 30 60 150 30 B, C B, C, D E, F H / J K H 1 J 30 An incomplete network for the activities is shown below. Complete the network, by adding in the missing edges. D, 30 O ), 30 K, 30 150 A, 30 Finish H, 60 B, 30 E 60 G, 30 Start Question 3 The network of roads between MLC and Ms Vernon's house is represented below. The numbers on the edges refer to the lengths of the roads in metres and the letters refer to intersections of the roads. 600 E 400 250 00E 450 400 250 200 MLC (M) 650 Ms Vernon's house (V) Ms Vernon takes a different route from her house (V) to MLC each day. Each route that she takes will need to pass through all the intersections. She wants to pass through each intersection once only. a. Name the type of walk that Ms. Vernon takes to MLC each day. (1 mark) b. State all the possible routes through the network of roads that would enable her to achieve this. (2 marks) c. Using your answer from part b, determine which of these routes covers the shortest distance. What is that shortest distance in metres? d. The Boroondara Council wants to do an upgrade on the Gas and Electricity connections in the same area, as shown in the network at the start of Question 3. For Gas, they plan to install natural gas pipes along each road. The Gas Company's engineers choose to follow an Eulerian path through the network of roads. 600 400 250 300 250 450 400 MLC 200 650 Ms Vernon's house D At which vertex should the gas pipe enter this network? (1 mark) e. For electricity, the council wants to install new streetlights at each intersection, with the power cable being placed underground. In order to keep costs down, the length of the power cable used should be a minimum. i. Show on the diagram below where the cable should be laid. 600 E 400 250 300 450 250 400 M 200 650 V (1 mark ii. What is the minimum length of cable required, in metres