2 Five successful applicants received the following scores when matched against suitability criteria for five jobs in a company.
| Job 1 | Job 2 | Job 3 | Job 4 | Job 5 |
| Alex | 13 | 11 | 9 | 10 | 13 |
| Bill | 15 | 12 | 12 | 11 | 12 |
| Cath | 12 | 10 | 8 | 14 | 14 |
| Don | 11 | 12 | 13 | 14 | 10 |
| Ed | 12 | 14 | 14 | 13 | 14 |
It is intended to allocate each applicant to a different job so as to maximise the total score of the five applicants.
- Explain why the Hungarian algorithm may be used if each number, \(x\), in the table is replaced by \(15 - x\).
- Form a new table by subtracting each number in the table from 15. Use the Hungarian algorithm to allocate the jobs to the applicants so that the total score is maximised.
- It is later discovered that Bill has already been allocated to Job 4. Decide how to alter the allocation of the other jobs so as to maximise the score now possible.