6. Three workers, \(\mathrm { P } , \mathrm { Q }\) and R , are to be assigned to three tasks, A, B and C. Each worker must be assigned to just one task and each task must be assigned to just one worker.
Table 1 shows the cost of using each worker for each task. The total cost is to be minimised. \begin{table}[h] \end{table}

1. Formulate the above situation as a linear programming problem. You must define your decision variables and make the objective and constraints clear.
   You are not required to solve the problem. Table 2 shows the profit gained by using each worker for each task. The total profit is to be maximised. \begin{table}[h]

   	Task A	Task B	Task C
   Worker P	33	37	31
   Worker Q	32	36	40
   Worker R	41	35	38

   \captionsetup{labelformat=empty} \caption{Table 2}
   \end{table}
2. Modify Table 2 in the answer book so that the Hungarian Algorithm could be used to find the maximum total profit. You are not required to solve the problem.
   (2)
   (Total 9 marks)