This study presents an investigation of an optimal slope design in the second degree Kronecker model for mixtureexperiments in four dimensions and its application in blending of selected fruits to prepare punch. The study centersaround weighted centroid designs, with the second degree Kronecker model. This is guided by the fact that the class ofweighted centroid designs is a complete class in the Kiefer Ordering. To overcome the problem of estimability, aconcise coefficient matrix is defined that aid in selecting a maximal parameter subsystem for the Kronecker model. Theinformation matrix of the design is obtained using a linear function of the moment matrices for the centroids anddirectly linked to the slope matrix. The discussion is based on Kronecker product algebra which clearly reflects thesymmetries of the simplex experimental region. From the family of matrix means, a well-defined function is used todetermine optimal values of the efficient developed design. Finally, a demonstration is provided for the case where thedesign is applied in fruit blending.
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