9.34. Suppose that you must design an experiment with six categorical factors. Factor A has six levels, factor B has five levels, factor C has five levels, factor D has three levels, and factors E and F have two levels. You are interested in main effects and two-factor interactions.

(a) How many runs are required to estimate all of the effects that are of interest?

(b) Find a D-optimal design that is suitable for this problem.

(c) Suppose that the experimenter decides that this design requires too many runs. What strategy would you recommend?