  Consider an experiment with a finite set of design points representing
permissible trial conditions. Suppose that each trial is associated with a cost
that depends on the selected design point. In this paper, we study the problem
of constructing an approximate D-optimal experimental design with simultaneous
restrictions on the size and on the total cost. For the problem of
size-and-cost constrained D-optimality, we formulate an equivalence theorem and
rules for the removal of redundant design points. We also propose a simple
monotonically convergent "barycentric" algorithm that allows us to numerically
compute a size-and-cost constrained approximate D-optimal design.
