Pearson Edexcel Level 3 GCE.. Further Mathematics Advanced Subsidiary Further Mathematics options 28: Decision Mathematics 2 (Part of option K only

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Write your answers in the answer book provided. 1. Five workers, A, B, C, D and E, are available to complete four tasks, P, Q, R and S. Each task must be assigned to exactly one worker and each work... er can do at most one task. Worker B cannot be assigned to task R. The amount, in pounds, that each worker will earn if they are assigned to each task is shown in the table below. P Q R S A 55 56 58 57 B 60 61 – 64 C 59 60 62 63 D 64 66 71 69 E 65 68 72 66 The Hungarian algorithm is to be used to find the maximum total amount that can be earned by the five workers. (a) Explain how the table should be modified to allow the Hungarian algorithm to be used, giving reasons for your answer. (2) (b) Reducing rows first, use the Hungarian algorithm to obtain the maximum possible total earnings. You should explain how any initial row and column reductions were made and how you determined if the table was optimal at each stage. (7) (Total for Question 1 is 9 marks) [Show More]

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