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

(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)?