For the basic feasible solution to remain optimal, A)all c_j − z_j values must remain ≤ 0. B)no objective function coefficients are allowed to change. C)the value of the objective function must not change. D)All of these are correct.

Question

Quizplus · Accepted Answer

In order for the basic feasible solution to remain optimal, we need to ensure that the values of the basic variables (i.e. the variables corresponding to the non-zero values in the optimal solution) do not change. This means that the values of the non-basic variables must change in such a way as to keep the basic variables at their optimal values. To achieve this, we need to make sure that all c_j − z_j values remain ≤ 0, as this ensures that increasing any non-basic variable will not result in a better solution. Therefore, choice A is the correct answer. Choices B and C are incorrect because they are too restrictive and do not take into account the possibility of changes to the non-basic variables that do not affect the optimal solution.

For the Basic Feasible Solution to Remain Optimal