Applications of necessary and sufficient conditions for maximin efficient designs

General sufficient and necessary conditions for minimax design are here reconsidered in a form allowing application in various optimal design problems. In combination with the Elfving theorem they are used to find maximin efficient designs for a two-dimensional linear extrapolation, and to find the optimum design for estimating the maximum point of a quadratic response function with intercept. An alternative proof of a recently published relation between D-optimality and maximin efficiency is given. It is shown that for exponential growth curve models with one parameter, maximin efficient designs can not be one point designs. A similar result is obtained for growth curve models with two parameters.