Experimental Design based on Box Problem Handout, problems 34, 36. A consulting firm engaged in road-building work is asked by one of its clients to determine the effects of six variables on the physical properties of a certain type of asphalt. Call these variables A, B, C, D, E, F. a) If a full two-level factorial design was used, how many runs would be made? b) Write a two-level resolution IV fractional factorial design requiring only 16 runs. By this, I mean that you should give the defining relation for this design. c) Is the design you gave in b) unique? (ie, could you find other fractions requiring the same number of runs, having the same resolution, but with different words in the defining relation?) d) In your design, what effects are aliased with the effect of A? With the effect of BD? e) Now assume that a second fraction of the same size is run, with the +/- pattern for A reversed, but with the +/- patters for B, C, D, E, and F kept the same. These 16 new runs give a new quarter fraction. What is the defining relation for this new fraction? f) If we combine the runs from the experiments described in b) and e), 32 runs will have been made. What is the defining relation for these 32 runs?