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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 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 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 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 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 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 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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