Optimal steady-state conditions are determined for the six operating modes of the industrial challenge problem proposed by Downs and Vogel. The problem is formulated as a nonlinear program with 50 variables and 44 nonlinear constraints. It uses the full state vector from the Downs and Vogel FORTRAN code, and thus is not a demonstration of optimization in a plant environment. Solutions are obtained using MINOS 5.1. The results show that the base case provided by Downs and Vogel is far from optimal. The operating cost (primarily purge losses) is easily reduced by more than 30%. In general, reactor pressure and liquid level should be held at their upper and lower bounds, respectively. Steam use can be eliminated, and the agitator speed can be fixed at its upper bound. The compressor recycle valve is closed in four of the six cases (the exceptions being the two cases requiring production of 90/10 G/H). Production can be increased by 59% for the 50/50 G/H product, but only by 4% and 12% in the 10/90 and 90/10 cases, respectively (relative to the nominal rates). Product rates are limited by reactant E for the 10/90 case, and by D otherwise. Most process variables change significantly with operating mode, and should not be held at constant setpoints. Other factors related to process control are discussed.