Incorporation of Predictive Milk Yield and Dry Matter Intake Equations into a Maximum-Profit Ration Formulation Program

Predictive equations for milk yield and dry matter intake derived from research observations were incorporated into a linear programming model to develop a computerized maximum-profit ration formulation program. To incorporate these nonlinear equations into a linear model, a feasible production response surface was identified and divided into four smaller segments which were defined more adequately by linear equations. Production activities for dry matter units with varying amounts of concentrate and crude protein then were calculated. These activities reflected changes in milk yield in the middle of each production segment as crude protein and concentrate content varied. They were incorporated into a matrix with several types of feed ingredients. Minimum and maximum nutrient constraints outlined by the National Research Council and other research were incorporated into the matrix. The final solution was obtained by allowing the program to solve through one segment of the production response surface, accumulating results, then reformulating a ration for the next segment with the process continuing till maximum differences between milk sales and feed cost was reached.