1. (100 points) Omzig, Inc produces 3 different widgets: a. type 1, which undergoes operations at machine A, then D, then C; b. type 2, which undergoes operations at machine E, then B, then C; c. type 3, which undergoes operations at machine D, then B, then A. The (centers of) machines A, B, C, D, and E are located at (x,y)-coordinates (10, 15), (20, 40), (60, 30), (35, 15), and (5, 40), respectively, in feet. See Figure 1 below. Widget Number of Units That Can Be Annual Demand 1 10,000 Transported in One Trip 10 2 14,500 5 3 8,000 20 E B D C Figure 1 a. (20 points) Give the asymmetric flow matrix (#trips/year). Assume 0% scrap rates. b. (60 points) Calculate the distance matrix for each of these distance measures: Euclidean, Rectilinear, and Tchebychev. c. (20 points) If rectilinear distances are used and the parameter Cij (defined in the course notes) equals one cent per foot, what is the "usual" objective function for the layout in Figure 1?