A non-linear mathematical farm business optimisation model, that is set within a spatial economic framework, has been developed. The model incorporates factors such as location, spatial market orientation and technology use, and identifies the business strategy that is optimal in different market and policy environments. Farm household time-use is incorporated centrally within the model, enabling it to examine how on-farm and off-farm activities compete for limited farm household human resources. The model is applied to a beef and sheep farm that can choose between selling livestock to meat processors or processing on-farm and selling direct to consumers. Model simulations reveal when it is optimal for the farm business to innovate in this way and how this decision is affected by changes in key parameters. The farm business model is solved using the GAMS/LINDOGlobal mathematical programming software package. While traditional nonlinear programming and mixed-integer nonlinear programming algorithms are guaranteed to converge only under certain convexity assumptions, GAMS/LINDOGlobal finds guaranteed globally optimal solutions to general nonlinear problems. The model and model results are discussed within the context of theoretical underpinnings, model tractability, and potential applications.