The range of optimality for a basic variable defines the objective function coefficient values for which that variable will remain part of the current optimal basic feasible solution.

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This statement is true. The range of optimality for a basic variable determines the values of its corresponding objective function coefficient for which it remains a part of the optimal basic feasible solution. In other words, if the objective function coefficient of a basic variable falls outside its range of optimality, the current optimal solution will no longer remain optimal and the variable will need to be replaced by a non-basic variable.

The Range of Optimality for a Basic Variable Defines the Objective