In agricultural economics, several calibration and aggregation approaches have evolved in mathematical programming models. This article combines in a linear programming model features of the Positive Mathematical Programming method with an aggregation approach that is constrained to the production possibility set spanned by a convex combination of observed production activities. The combination is obtained by using a variable separation technique that approximates a non-linear objective function. Therefore, linear programming models can be exactly calibrated to observed production activities. The aggregation of production activities in homogenous production response units assumes that farmers in a region are treated such as they respond in the same way. Both methodologies are embedded in economic reasoning and provide a robust framework to solve large-scale linear programming models in reasonable time.