Edexcel D2 2014 June — Question 6

Exam BoardEdexcel
ModuleD2 (Decision Mathematics 2)
Year2014
SessionJune
TopicPermutations & Arrangements
TypeOptimization assignment problems

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.
1234
A29153230
B34264032
C282735-
D-213331
Formulate the above situation as a linear programming problem. You must define your decision variables and make the objective function and constraints clear.