Suppose that you need to design an experiment for five factors. Three of these factors are categorical with three levels and the remaining two factors are continuous. You are interested in the main effects and the two-factor interactions of all factors, along with the pure quadratic effects of the two continuous factors.

(a) How many runs are required for this experiment?

(b) Construct a D-optimal design with the minimum number of runs. What are the relative variances of the model parameters?

(c) Construct an I-optimal design with the minimum number of runs. What are the relative variances of the model parameters? How does this design compare to the D-optimal design you constructed in part (b)?