an experimenter wishes to study seven variables at two levels each and chooses to do so with a 32-run resolution IV design with the generators I=12346 and I = 12457. A colleague argues that he can achieve the same resolution with a design that employs only 16 runs. Is the colleague correct? If so, write down generators and the defining relation for such design. Write out all of the linear combinations of effects that can be estimated for each design. Comment on the relative merits of each design