2 A company has organised four regional training sessions to take place at the same time in four different cities. The company has to choose four of its five trainers, one to lead each session. The cost ( \(\pounds 1000\) 's) of using each trainer in each city is given in the table.
| \multirow{7}{*}{Trainer} | \multirow{2}{*}{} | City |
| | London | Glasgow | Manchester | Swansea |
| Adam | 4 | 3 | 2 | 4 |
| Betty | 3 | 5 | 4 | 2 |
| Clive | 3 | 6 | 3 | 3 |
| Dave | 2 | 6 | 4 | 3 |
| Eleanor | 2 | 5 | 3 | 4 |
- Convert this into a square matrix and then apply the Hungarian algorithm, reducing rows first, to allocate the trainers to the cities at minimum cost.
- Betty discovers that she is not available on the date set for the training. Find the new minimum cost allocation of trainers to cities.