Abstract:The Second order kronecker model for simplex-centroid design was fitted where data was for feed supplements blend using a mixture of soya beans, maize jam, cotton seed and fish meal guided by design points in the simplex-centroid design and the respose was the yield of milk in litres. The main objective was to fit a Kronecker model in the simplex-centroid design to formulate optimum dairy meal concentrates. Use the data to fit the second order kronecker model for four components simplex-centroid design. From the Kronecker regression function, coefficient matrix was derived from selected parameter subsystem of interest, moment matrix was then obtained. Information matrix and improved information matrix were derived. The collected data was fitted in the derived Kronecker model and the estimates of the parameters as well as overall model performance were numerically obtained. ANOVA was run to incorporate the constant term. From the analysis it was found that Kronecker model provided a good fit. Therefore the results support that the feed supplement had significant effect to milk productivity. For optimal production the research recommend that more than one ingredients need to be blend. Blends with soya beans and fish meal in two, three and four ingredients were statistically significant and therefore recommended for optimal milk production. From the ANOVA it was found that other factors not included in this study affect milk productivity and therefore the research recommends further studies be done to investigate those other factors such as the breeds, feeding practices and also effect of supplement to other dairy products.