The problem of designing contaminated groundwater remediation systems using hydraulic control is addressed. Two nonlinear optimization formulations are proposed which model the design process for the location and pump rates of injection and extraction wells in an aquifer cleanup system. The formulations are designed to find a pumping system which (1) removes the most contaminant over a fixed time period and (2) reduces contaminant concentration to specified levels by the end of a fixed time period at least cost. The formulations employ a two-dimensional Galerkin finite element simulation model of steady state groundwater flow and transient convective-dispersive transport. To make the optimization problems computationally tractable sensitivity theory is used to derive a general relationship for computing the derivatives of an arbitrary function of the simulation outputs with respect to model inputs. This relationship is then applied to the convective-dispersive transport equation.