- Five workers, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D }\) and E , are to be assigned to five tasks, \(1,2,3,4\) and 5 . Each worker is to be assigned to one task and each task must be assigned to one worker.
The cost, in pounds, of assigning each person to each task is shown in the table below. The cost is to be minimised.
| 1 | 2 | 3 | 4 | 5 |
| A | 129 | 127 | 122 | 134 | 135 |
| B | 127 | 125 | 123 | 131 | 132 |
| C | 142 | 131 | 121 | 140 | 139 |
| D | 127 | 127 | 122 | 131 | 136 |
| E | 141 | 134 | 129 | 144 | 143 |
- Reducing rows first, use the Hungarian algorithm to obtain an allocation that minimises the cost. You must make your method clear and show the table after each stage.
- Find the minimum cost.