A model of live performance is presented that includes simplified acoustic-environmental system models and enables the coupling behavior between multiple sources and receivers to be predicted. The model allows the mix at each location within the performance space to be evaluated as a function of the acoustic signals generated by the instruments and of the control parameters on the mixing desk, through which the instrument signals are sent before being reinforced using loudspeakers. For a set of listener locations, which includes both performers and members of the audience, ideal mixes are defined, and an optimization algorithm is developed that sets the control parameters on the mixing desk automatically, to deliver approximations of these ideal mixes to all listener locations simultaneously. The control parameters are constrained during the optimization to prevent the onset of acoustic feedback. The algorithm is examined, and we show that a targeted approach, which first sets the control parameters relating the vocal level, gives a better solution in a shorter time when compared to a brute-force approach.