This article describes a linear penalty method for getting sensitive information, i.e. the effect of variation on the constraint to the objective function. The dynamic optimization problem discussed here is a problem with state constraints. At first, the problem is formulated to unconstrained dynamic optimization problem by adding the constraints to the objective function as linear penalty terms. Then, the mathematical formulas to evaluate the change in the objective function and the optimal solution is derived if small perturbation introduced in the constraints. Lastly, the numerical simulation is done to show the effectiveness of the method.