The assignment problem constraint x₃₁ + x₃₂ + x₃₃ + x₃₄ ≤ 2 means A)agent 3 can be assigned to two tasks. B)agent 2 can be assigned to three tasks. C)a mixture of agents 1,2,3,and 4 will be assigned to tasks. D)there is no feasible solution.

Question

Quizplus · Accepted Answer

The constraint states that the sum of the decision variables for agent 1 and task 31, agent 1 and task 32, agent 1 and task 33, and agent 1 and task 34, is less than or equal to 2. This means that agent 1 can only be assigned to at most two of these tasks. Therefore, it cannot be agent 2 that can be assigned to three tasks as stated in choice B, nor can it be a mixture of agents 1, 2, 3, and 4 as stated in choice C. The only feasible solution is that agent 3 can be assigned to two tasks as stated in choice A. There is no information to suggest that there is no feasible solution, so choice D is incorrect.

The Assignment Problem Constraint X31 + X32 + X33

The Assignment Problem Constraint X₃₁ + X₃₂ + X₃₃