Abstract: D-optimal and c-optimal designs for binary response experiments with two design variables are considered. It is shown that with two design variables and a bounded design space, there exists a D-optimal design which has at most four or six symmetrically arranged support points, from which further reduction in the number of support points may sometimes be accomplished by using an asymmetric weighting. For c-optimality we identify when the support consists of 1, 2 or 3 points. The amount of numerical work required does not differ from the one design variable case.
Key words and phrases: Binary data, convex hull, logit, optimal design, probit.