2 The following table shows the times taken, in minutes, by five people, Ash, Bob, Col, Dan and Emma, to carry out the tasks 1, 2, 3 and 4 . Dan cannot do task 3.
| Ash | Bob | Col | Dan | Emma |
| Task 1 | 14 | 10 | 12 | 12 | 14 |
| Task 2 | 11 | 13 | 10 | 12 | 12 |
| Task 3 | 13 | 11 | 12 | ** | 12 |
| Task 4 | 13 | 10 | 12 | 13 | 15 |
Each of the four tasks is to be given to a different one of the five people so that the overall time for the four tasks is minimised.
- Modify the table of values by adding an extra row of non-zero values so that the Hungarian algorithm can be applied.
- Use the Hungarian algorithm, reducing columns first then rows, to decide which four people should be allocated to which task. State the minimum total time for the four tasks using this matching.
- After special training, Dan is able to complete task 3 in 12 minutes. Determine, giving a reason, whether the minimum total time found in part (b) could be improved.
(2 marks)