In this paper D- and V-optimal population designs for the quadratic regression model with a random intercept term and with
values of the explanatory variable taken from a set of equally spaced, non-repeated time points are considered. D-optimal
population designs based on single-point individual designs were readily found but the derivation of explicit expressions for
designs based on two-point individual designs was not straightforward and was complicated by the fact that the designs now
depend on ratio of the variance components. Further algebraic results pertaining to d-point D-optimal population designs where
dZ3 and to V-optimal population designs proved elusive. The requisite designs can be calculated by careful programming and
this is illustrated by means of a simple example.