Why is it important to understand the range of optimality?

Understanding the range of optimality is crucial in linear programming as it provides insight into how variations in the objective function coefficients affect the optimal solution. This range indicates the limits within which the current optimal solution remains unchanged when the coefficients of the objective function are modified.

When a decision-maker is aware of this range, they can confidently assess the robustness of the current solution against potential changes in costs or profits. For instance, if the coefficients representing costs change due to market fluctuations, knowing the range of optimality would allow the decision-maker to determine whether the existing optimal solution is still valid or if adjustments need to be made. This understanding helps in making informed decisions under uncertainty and aids in sensitivity analysis, which is vital for effective decision-making in various applications of linear programming.

The other options do not directly address the primary significance of the range of optimality in relation to optimal solutions and their stability under variations in coefficients.