Optimum designs for optimum mixtures

In a mixture experiment, the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffé [1958. Experiments with mixtures. J. Roy. Statist. Soc. B 20, 344-360; 1963. Simplex--centroid design for experiments with mixtures. J. Roy. Statist. Soc. B 25, 235-263] first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. However, in a mixture experiment, often one is more interested in the optimum proportion of ingredients. In this paper, we try to find optimum designs for the estimation of optimum mixture combination on the assumption that the response function is quadratic concave over the simplex region.