Optimal designs specify design points to use and how to distribute subjects over these design points in the most efficient manner. The Hill model with three parameters is often used to describe sigmoid dose response functions. In our paper, we study optimal designs under the Hill model. The first is D-optimal design, which works best to study the model to fit the data. Next is c-optimal design, which works best to study a target dose level, such as ED50 - the dose level with 50% maximum treatment effect. The third is a two-stage optimal design, which considers both D-optimality and c-optimality. In order to compare the optimal designs, their design efficiencies are compared.