This paper deals with some optimal control problems associated with the equations of steady-state, incompressible magnetohydrodynamics. These problems have direct applications to nuclear reactor technology, magnetic propulsion devices, and design of electromagnetic pumps. These problems are first put into an appropriate mathematical formulation. Then the existence of optimal solutions is proved. The use of Lagrange multiplier techniques is justified and an optimality system of equations is derived. The theory is applied to an example.