Mixture experimental designs have been widely used in industrial and agricultural production, scientific experiment and daily life. The traditional mixture experimental designs are generally implemented under the assumption that the experimental errors are homosce-dastic, but heteroscedastic errors are relatively more accordant with practical circumstances. In this paper, we mainly study the $D$-, $A$- and linear optimality of direct product designs for mixture product models under the assumption of heteroscedastic errors. It is shown that the $D$-, $A$- or linear optimal designs for mixture product models can be constructed from the corresponding optimal designs for their homogeneous sub-mixture models under given conditions.