6. Four workers, A, B, C and D, are to be assigned to four tasks, 1, 2, 3 and 4. Each worker must be assigned to just one task and each task must be done by just one worker.
Worker C cannot do task 4 and worker D cannot do task 1.
The cost of assigning each worker to each task is shown in the table below. The total cost is to be minimised.
| 1 | 2 | 3 | 4 |
| A | 29 | 15 | 32 | 30 |
| B | 34 | 26 | 40 | 32 |
| C | 28 | 27 | 35 | - |
| D | - | 21 | 33 | 31 |
Formulate the above situation as a linear programming problem. You must define your decision variables and make the objective function and constraints clear.