Abstract: This study examines optimal design problems in multiresponse linear models. We investigate the optimality, admissibility, and invariance of approximate designs. Necessary and sufficient conditions are given for a design to be admissible and invariant. Elfving's theorem for D-optimality is established for the multiresponse linear models.

Key words and phrases: Admissible design, Elfving's theorem, invariant design, multiresponse model, optimal design.