In standard Simplex tableaus, a maximization problem chooses the non-basic variable with the most positive net evaluation to enter until all values are, whereas a minimization problem selects the variable with the most negative net evaluation until all values are.

In the Simplex tableau, the entering variable selection criteria and optimality conditions differ because maximization and minimization target opposite directions of the objective function. For a maximization problem, the optimality condition requires all reduced costs in the objective row to be non-negative, and the algorithm selects the non-basic variable with the most negative coefficient to enter the basis because it provides the steepest rate of profit improvement. Conversely, for a direct minimization tableau, the optimality condition requires all reduced costs to be non-positive, and the algorithm selects the non-basic variable with the most positive coefficient to enter the basis, as this choice drives the cost function downward toward the optimal minimum value.

For maximization, choose a variable that increases the objective, while for minimization, choose one that decreases it.

For maximization, choose a variable with a negative reduced cost; for minimization, choose one with a positive reduced cost, depending on the tableau convention.

For maximization, choose an entering variable with a negative reduced cost (for the usual Cj−Zj convention), while for minimization, choose one with a positive reduced cost; optimality is reached when no coefficient can further improve the objective.

In a maximization problem, you select the entering variable with the most negative net evaluation value to increase profit. In a minimization problem, you select the variable with the most positive net evaluation value to reduce total cost. Optimality is reached when no further improving variables exist.

In the Simplex tableau, the entering-variable criterion depends on whether the problem is maximizing or minimizing. For a maximization problem, the variable with the most negative coefficient in the objective row (using the common Cj-Zj convention) enters because it can increase the objective value. For a minimization problem, the variable with the most positive coefficient enters because it can decrease the objective value. The process continues until there are no coefficients indicating further improvement, which means the current solution is optimal.