An industrial engineer is conducting an experiment using a Monte Carlo simulation model of an inventory system. The independent variables in her model are the order quantity (A), the reorder point (B), the setup cost (C), the backorder cost (D), and the carrying cost rate (E). The response variable is average annual cost. To conserve computer time, she decides to investigate these factors using a 2^5-2_m design with I = ABD and I = BCE. The results she obtains are de = 95, ae = 134, b = 158, abd = 190, cd = 92, ac = 187, bce = 155, and abcde 185.

(a) Verify that the treatment combinations given are correct. Estimate the effects, assuming three-factor and higher interactions are negligible.

(b) Suppose that a second fraction is added to the first, for example, ade = 136, e = 93, ab = 187, bd = 153, acd = 139, c = 99, abce = 191, and bcde = 150. How was this second fraction obtained? Add this data to the original fraction, and estimate the effects.

(c) Suppose that the fraction abc = 189, ce = 96, bcd = 154, acde = 135, abe = 193, bde = 152, ad = 137, and (1) = 98 was run. How was this fraction obtained? Add this data to the original fraction and estimate the effects.