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A linear programming model that accounts for the economic consequences of response to selection to the producer enterprise over a given planning horizon is described. A procedure is given in detail for defining upper and lower bounds constraints on variables that are correlated in the linear programming model. This procedure enabled the linear programming model to construct a feasible hyperspace that reflects the relationship between the variables in terms of the trend in the relationship and the variation around this trend. The linear programming model was used to compute optimal rates of response to selection for four planning horizons. The optimal response to selection per year for the production traits was closest to the maximums achievable from a gene-flow model. Of all the non-production traits, days open had the greatest proportion of its maximum achievable from a gene-flow model. The linear programming model was used to compute relative economic weights (REV) for the nine traits for each planning horizon. The REVs for milk, fat, and protein production were considerably larger than the REVs for the non-production traits for all planning horizons. Somatic cell score had the largest REVs of the non-production traits in all planning horizons.

Linear programming applied to dairy cattle selection