Recently, with advanced computational performance, numerical design optimization including CFD has been developed in aerospace engineering. However it could hardly find the design optimization softwares and contents of which educational purposes in aerospace engineering. In this study, inverse shape design is developed for steady, two dimensional inviscid and compressible flow over airfoils using aerodynamic design optimization framework for an airfoil based on EDISON_CFD(Education-research through Simulation On the Net for Computational Fluid Dynamics). Design optimization is performed for drag minimization in transonic flow. Two target pressure distributions are RAE2822 known as transonic airfoil and previously designed airfoil for drag minimized from NACA0012 airfoil. Both result showed that shape, lift coefficient, and drag coefficient of baseline airfoil got closer to those of target airfoil. From a result, contents of design optimization framework could be expected to help in the lecture.