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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 The activity times in the project network shown are in days. Key (for activity E) -Latest start time ; E 5 Earliest start time “Time to complete Finish The greatest float time for a non-critical activity in this network is (A) 2 days. (B) 4 days. (C) 5 days. (D) 12 days.
QUESTION 21 (5 marks) This network shows the maximum number of supplies (in tonnes) that can be transported from a warehouse to a cyclone shelter along each road each day during an emergency. A 50 20 Warehouse Cyclone shelter 40 30 € a) Use the ‘maximum flow minimum cut’ theorem to determine the maximum amount of supplies that can reach the cyclone shelter each day. [3 marks] b) During a cyclone the intersection at vertex A is damaged and no longer allows for any supplies to pass through it. What is the new maximum amount of supplies each day that can reach the cyclone shelter? [2 marks]
QUESTION 5 (5 marks) A company has three tasks to allocate to three contractors. Each of the contractors has a quote recorded for each task shown in the table. The quotes are in thousands of dollars ($°000s). Contractor‘ 1PN Q ‘ Task 2 ‘ Task 3 Use a matrix method to determine the minimum cost if each contractor is allocated one task.
QUESTION 6 (7 marks) A company needs to complete the following project as quickly as possible. Each task can only be completed by a single employee and must be completed before that employee can start the next task. The owner believes that this project can be completed in minimal time with only three employees. Evaluate the reasonableness of this belief.
QUESTION 5 The coach of a four-person relay team is deciding on the order of the runners. Use the bipartite graph to determine which statement 1s correct. Simon first runner Balal second runner Ivan third runner Linh fourth runner (A) Linh should be the first runner. (B) Simon should be the second runner. (C) Ivan should be the third runner. (D) Balal should be the fourth runner.
QUESTION 7 Which cut (C; C C5or Cy) could be used to determine the maximum flow from the source to the sink in this network? Cnl C Z C\\3 C4 90 | Source Sink Not to scale (55 (A) C B) G C) G (D) C4
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 13 Based on this project network what is the minimum number of days required to complete the project? (A) 16 (B) 17 (©) 19 (D) 31
QUESTION 19 (5 marks) The activity table for a project is shown. Activity Prerequisite Time activity (days) a) b) ©) Use the activity table to construct a network diagram including earliest and latest starting times. [3 marks] Determine the critical path. [1 mark] Determine the shortest completion time for the project. [1 mark]
QUESTION 23 (4 marks) The network diagram shows the flow of water from the tank (source) to the kitchen tap (sink). L L L L Not to scale Tank ] D . 15 E a) Explain which dashed line (L L L; or L) 1s not a valid cut. [1 mark] b) Calculate the capacity of each dashed line that is a valid cut. [3 marks]
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 6 (7 marks) A tow truck company has three tow trucks (A B and C) and receives calls from three motorists (P Q and R) who have broken down. The network shows the distances in kilometres (km) from each of the tow trucks to each of the motorists where x represents the distance between Tow Truck C and Motorist P. Not to scale The minimum total distance travelled by the three tow trucks in order for each tow truck to visit exactly one motorist 1s 32 km. Use the Hungarian algorithm to determine the distance between Tow Truck C and Motorist P.
QUESTION 1 The float time in minutes for the non-critical activity of this project network is Watch the news 10 min ‘Collect Turn on 'Prepare 'Cook qp Eat @b ingredients oven ingredients food food 3 min 5 min 8 min 17 min 5 min (A) 10 (B) 20 ) 23 (D) 30
QUESTION 7 This matrix was obtained after applying the Hungarian algorithm to determine the optimal allocation of three people Elandra (E) Farid (F) and Grace (G) to three tasks: legal (L) monitoring (M) and verification (V). L M V E|0 0 7 F|0 3 8 G|1 O O The optimal allocation is (A) EtoV FtoMand Gto L. (B) EtoV FtoLandGtoM. (C) EtoM FtoLand Gto V. (D) EtoM FtoVand GtoL.
QUESTION 9 Identify the graph that is a spanning tree. (A) o @) wn ~e ©) o &) = (B) (D) )—U w2 o 2 ( = ( =
QUESTION 20 (4 marks) The table summarises the distances in kilometres (km) between three flower stores and three delivery locations: A B and C. Use the Hungarian algorithm to determine the minimum total distance needed to deliver flowers to all locations if each store delivers flowers to only one location. A B | C Store 1 24
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 The duration in minutes of all activities in a project are shown. Activity pe yTefTe[s|;rpeyy The critical path for the project is PRSV. What is the earliest completion time for the project if it starts at 11:00 am? (A) 12:30 pm (B) 1:10pm (C) 1:30pm (D) 2:10 pm
QUESTION 8 Activities P and Q are the critical activities for a project. Activity Prerequisite activity
QUESTION 21 (4 marks) The road network shows the number of vehicles per hour travelling from the airport to the town centre. cut X _ College Airport Town centre \ Showground a) Determine the capacity of cut X. b) Determine the maximum flow from the airport to the town centre. [1 mark] [2 marks]
QUESTION 24 (5 marks) Jed is preparing and serving a meal of curry and rice with naan bread. The table shows the duration and prerequisites for all the tasks they must complete. Task description Duration (minutes) Prerequisite Assemble equipment 2 — Boil rice 20 Prepare curry ingredients 6 Simmer curry 40 Fry naan bread + Serve meal 2 |B Do Make naan bread 8 a) Construct a network diagram to show the sequence of tasks from start to finish labelling all tasks and durations. Use forward and backward scanning to show the earliest and latest starting times for all tasks. [3 marks] b) Determine the critical activities and minimum completion time for preparing and serving the meal. [2 marks]
QUESTION 1 (5 marks) A triathlon relay has three sections: swim (S) cycle (C) and run (R). The matrix shows the average number of minutes for three athletes Jane (J) Knox (K) and Levi (L) to complete each section. S C R J|40 56 66 K/ 36 60 72 L/}25 48 78 Use the Hungarian algorithm to predict the minimum total relay time if assigning each athlete to completing one section.
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 8 Activities A B C D E F G H and J must be completed for the project shown in the network. Activity times are in minutes. G 7 Start Finish The earliest starting time in minutes for Activity J on the network diagram above is A) 16 (B) 15 C) 13 (D) 11
QUESTION 16 Determine the value of the cut made on the network diagram below. B 70 E<—Cut (A) 160 (B) 170 (C) 180 (D) 240
QUESTION 30 (4 marks) The network diagram below illustrates the time taken in days for 10 different activities labelled A—K involved in the completion of a task. H 10 E 2 a) Identify the critical path for the diagram above. [1 mark] b) Calculate the latest starting time for Activity G. [1 mark] c) Calculate the float time for Activity E. [2 marks]
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]
QUESTION 5 (8 marks) Kate Luca and Marcel are carpenters. Each carpenter needs to build one piece of furniture: a bookcase a chair or a desk. As each carpenter works at a different rate the table below shows the total cost for each carpenter to build each piece of furniture. a) Use the Hungarian algorithm to determine who should build each piece of furniture to minimise the total cost. [5 marks] b) Evaluate the reasonableness of your solution to 5a). [3 marks]
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