In a Linear Programming Problem Involving Two Decision Variables,a Change

In a linear programming problem involving two decision variables,a change in one of their coefficients will:

A) always change the optimal solution since the slope of the objective function changes.
B) typically change the feasible region till a stage,beyond which the constraint functions become nonbinding.
C) never change the optimal solution as the other coefficient is still fixed.
D) change the optimal solution only if the slope of the objective function's contour changes significantly.
E) their shadow prices although the constraints are not affected directly.