1 Four friends have rented a house and need to decide who will have which bedroom. The table below shows how each friend rated each room, so the higher the rating the more the room was liked.
| | | | |
| Phil | 5 | 1 | 0 | 4 |
| Rob | 1 | 6 | 1 | 2 |
| Sam | 4 | 2 | 2 | 3 |
| Tim | 3 | 5 | 0 | 0 |
The Hungarian algorithm is to be used to find the matching with the greatest total. Before the Hungarian algorithm can be used, each rating is subtracted from 6.
- Explain why the ratings could not be used as given in the table.
- Apply the Hungarian algorithm, reducing rows first, to match the friends to the rooms. You must show your working and say how each matrix was formed.