The performed two step procedure was motivated in Section 3.2 to ensure that the stage-to-stage calculations can always be performed. If the optimization problem is directly solved without additional iequalities, the stage-to-stage calculations may be unstable. If they fail too often, the solver may not converge to an optimal or even feasible solution. In this easy example the initial values calculated with the V min diagram are already quite close to the final solution. This is why we tried to solve the optimization problem directly without the additional inequalities. The solver had some difficulties but converged after 102 iterations (65.25 seconds) to the same optimal solution. In 29 of the iterations the stage-to-stage calculations failed which was handled by a forced step back in the line-search of the sqp-algorithm. In this example, it is in principle possible to avoid the two step procedure. However, the solver needed more iterations and more time. The failures in the evaluations show that it is more difficult to solve the problem directly and it can beneficial to follow the proposed two step procedure.