Pearson Edexcel Level 3 GCE 2023 Further Mathematics Advanced Subsidiary Further Mathematics options 28: Decision Mathematics 2 (Part of option K only) Question Paper and Mark Scheme Merged

1. Five workers, A, B, C, D and E, are available to complete four tasks, P, Q, R and S. Each worker can only be assigned to at most one task, and each task must be done by at most one worker. Worker B cannot be assigned to task Q and worker E cannot be assigned to task S. The time, in minutes, that each worker takes to complete each task is shown in the table below. P Q R S A B 39 – 39 40 C D E 36 39 41 – The Hungarian algorithm is to be used to find the least total time to complete all four tasks. (a) Explain how the table should be modified so that the Hungarian algorithm can be applied. (2) (b) (i) Use the Hungarian algorithm to obtain an allocation that minimises the total time. (ii) Explain how you determined if the table was optimal at each stage. (6) (c) Calculate the least total time to complete all four tasks.