The objective of this study is to develop a reliable and efficient design tool that can be used in hypersonic flows. The flow analysis is based on the axisymmetric Euler and the finite rate chemical reaction equations. These coupled equations are solved by using Newton's method. The analytical and numerical methods are used to calculate Jacobian matrices. The effects of error in numerical Jacobians on the performance of flow and sensitivity analyses are studied. A gradient based numerical optimization is used. Sensitivities are calculated by using finite-difference, direct differentiation and adjoint methods. The objective of the design is to generate a hypersonic blunt geometry that produces the minimum pressure drag while keeping the maximum temperature smaller than the initial value. Bezier curves are used for geometry modification. The performance of the optimization method is demonstrated for different hypersonic flow conditions.