D2 June 2011 Q6

EdexcelOld spec9 marksAllocation

6. Three workers, P, 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.

Task ATask BTask C
Worker P273125
Worker Q263034
Worker R352932

Table 1

(a) 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. (7)

Table 2 shows the profit gained by using each worker for each task. The total profit is to be maximised.

Task ATask BTask C
Worker P333731
Worker Q323640
Worker R413538

Table 2

(b) 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)
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