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QUESTION 7 What is the length of the minimum spanning tree for this network? All distances are in kilometres (km). (A) 22km (B) 14 km (C) 12km (D) 3 km
QUESTION 12 Which statement is correct? (A) A minimum spanning tree must contain a loop. (B) A minimum spanning tree must contain a cycle. (C) Every network has only one minimum spanning tree. (D) A minimum spanning tree has one more vertex than the number of edges.
QUESTION 2 (4 marks) All buildings in a school are connected by underground electricity cables indicated by the network. All measurements are in metres. Admin Class 1 Sports shed Class 4 Tuckshop Not to scale 60 The electricity cables need replacing and will cost $1200 per metre. The school wants to minimise costs by replacing the shortest length of cable necessary to connect all buildings. If the school has a budget of $155 000 evaluate whether they can afford this project.
QUESTION 9 Identify the graph that is a spanning tree. (A) o @) wn ~e ©) o &) = (B) (D) )—U w2 o 2 ( = ( =
QUESTION 5 (5 marks) The map details the length (in metres) of paths between nine key locations in a theme park. The annual cost to maintain the paths is $214 per metre. The theme park manager believes at least $138 000 can be saved each year if some paths are removed while still allowing visitors to access every key location using paths. Roller- coaster Ferris 170 Wheel Car park Eatlng area 05 T 6 60 Toilet Bumper Stunt 170 cars h show 185 165 65 Water slide Laser Not to scale show Evaluate the reasonableness of the manager’s belief.
QUESTION 3 (5 marks) The diagram represents a network of 10 ski stations connected by chairlift cables. The length (km) of each cable is shown except for cable C which is closed for maintenance. When cable C reopens the minimum total cable length required to connect all stations will decrease by | km. Determine the length of cable C and the minimum total cable length required to connect all stations when cable C reopens.
QUESTION 1 Identify a minimum spanning tree from the diagrams below. (A) (B)
QUESTION 2 (4 marks) A cable company is calculating the cost of laying cable between five houses (A B C D and E). The unit cost of laying the cable is $2.50 per metre. The shortest distances (in metres) between the houses are shown below. a) Construct a network diagram to represent the distances between the houses in the space provided below. [1 mark] b) Determine the minimum cost to connect all of the houses. [3 marks]
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