3. Five friends have rented a house that has five bedrooms. They each require their own bedroom. The table below shows how each friend rated the five bedrooms, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D }\) and E , where 0 is low and 10 is high.
| A | B | C | D | E |
| Frank | 5 | 0 | 7 | 3 | 4 |
| Gill | 5 | 3 | 8 | 10 | 1 |
| Harry | 4 | 3 | 7 | 9 | 0 |
| Imogen | 6 | 3 | 6 | 5 | 4 |
| Jiao | 0 | 2 | 7 | 3 | 2 |
Reducing rows first, use the Hungarian algorithm to obtain an allocation that maximises the total of all the ratings. You must make your method clear and show the table after each stage.
(Total 8 marks)