The most suited air breathing vehicle to hypersonic flight is the supersonic combustion ramjet, or scramjet. One of the many challenges to scramjets is being able to operate efficiently over a wide range of flight conditions. Under the extreme pressure and heat experienced at these flight conditions there is a high degree of shape uncertainty. Numerous phenomena such as inlet unstart, extreme load, boundary-layer effects and shear layer interaction, restrict scramjet design and limit their performance. Such problems are the main motivation for surface sensitivities that can be used for aerodynamic shape optimization. The objective of the present paper is to document lessons learned from aerodynamic shape optimization of the HiFire scramjet configuration under supersonic flow conditions. Mesh warping and geometry parametrization is accomplished by using surface control points embedded with free-form deformation (FFD) volumes. The aerodynamic model solves the RANS equations with Spallart-Almaras turbulence model. A gradient based optimization algorithm is used with an adjoint method in order to compute the objectives and constraints derivatives with respect to the design variables. The main purpose of this study is to suggest an approach for aerodynamic shape optimization of scramjet inlet and mainly to present two optimization problem formulations which includes different objectives: pressure recovery and thrust, by using a polynomial approach which reflects a low fidelity model of the combustion and expansion process. The results of optimization are presented, including the tradeoff between the two approaches.