- Four workers, A, B, C and D, are to be assigned to four tasks, P, Q, R and S. Each worker must be assigned to exactly one task and each task must be done by only one worker. The time, in hours, that each worker takes to complete each task is shown in the table below.
| \cline { 2 - 5 }
\multicolumn{1}{c|}{} | P | Q | R | S |
| A | 7.5 | 3.5 | 8 | 9.5 |
| B | 5 | 2 | 7 | 7.5 |
| C | 4 | 3.5 | 3.5 | 8 |
| D | 6 | 5 | 3.5 | 4 |
Reducing rows first, use the Hungarian algorithm to obtain an allocation which minimises the total time. You must explain your method and show the table after each stage.