7. Four workers, A, B, C and D, are to be assigned to four tasks, P, Q, R and S. Each worker is to be assigned to exactly one task and each task must be assigned to just one worker. The cost, in pounds, of using each worker for each task is given in the table below. The total cost is to be minimised.
| P | Q | R | S |
| A | 23 | 41 | 34 | 44 |
| B | 21 | 45 | 33 | 42 |
| C | 26 | 43 | 31 | 40 |
| D | 20 | 47 | 35 | 46 |
Formulate the above situation as a linear programming problem. You must define your decision variables and make the objective function and constraints clear.
(Total 7 marks)