Any coefficient change within these allowable ranges leaves the optimal decision variable values completely unchanged, though a basic variable's change will proportionally shift the total objective function value.

Put the new coefficient into the final simplex tableau and check if all non-basic reduced costs still satisfy the optimality condition. If any reduced cost violates its required sign, the optimal solution changes.

You determine this by calculating the allowable range for that coefficient from the final simplex tableau and checking if your proposed change stays within those limits.

Use the allowable increase/decrease from the final simplex tableau: if the new coefficient stays within its allowable range, the current optimal solution does not change, although the optimal objective value may change.

To determine whether changing an objective function coefficient will affect the current optimal solution, evaluate whether the coefficient belongs to a basic or nonbasic decision variable. For a nonbasic variable, changing its coefficient only affects its own reduced cost, so the current solution remains optimal as long as the new value does not cross its reduced cost threshold. For a basic variable, changing its coefficient alters the shadow prices and affects the reduced costs of all nonbasic variables simultaneously. If the updated coefficient stays within the allowable range computed from the optimal tableau, the optimal decision variable values remain unchanged, though the total objective value will change.

You can determine this by checking the allowable increase and allowable decrease of the objective function coefficient. If the new coefficient stays within this range, the current optimal solution remains the same. If it goes outside the range, the current optimal solution may change and the problem should be solved again.

You can determine this by checking the allowable increase and allowable decrease for the objective function coefficient in the sensitivity report; if the new coefficient stays within this range, the current optimal solution remains unchanged, but if it goes outside the range, the optimal solution may change.

Check the allowable increase and decrease for that objective coefficient in the sensitivity analysis. If the change stays within the allowable range, the current optimal solution remains unchanged.

You can determine this using sensitivity analysis by checking the coefficient’s allowable increase and allowable decrease. If the new objective coefficient stays within this range, the current optimal solution remains optimal, although the optimal objective value may change. If the coefficient goes outside the allowable range, the current solution may no longer be optimal, so the LP generally needs to be re-solved.