Omzig, Inc produces 3 different widgets: type 1, which undergoes operations at machine A, then D, then C; type 2, which undergoes operations at machine E, then B, then 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, 7.5), (20, 20), (60, 12.5), (35, 7.5), and (5, 20), respectively, in feet. See Figure 1 below. Widget Type 1 2 3 Annual Demand E A 10,000 14,500 8,000 B Number of Units That Can Be Transported in One Trip 10 5 20 D C Figure 1 a. (10 points) Give the asymmetric flow matrix (# trips/year). Assume 0% scrap rates. b. (30 points) Calculate the distance matrix for each distance measure: (1) Euclidean, (2) rectilinear, and (3) Tchebychev. c. (10 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? Omzig, Inc produces 3 different widgets: type 1, which undergoes operations at machine A, then D, then C; type 2, which undergoes operations at machine E, then B, then 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, 7.5), (20, 20), (60, 12.5), (35, 7.5), and (5, 20), respectively, in feet. See Figure 1 below. Widget Type 1 2 3 Annual Demand E A 10,000 14,500 8,000 B Number of Units That Can Be Transported in One Trip 10 5 20 D C Figure 1 a. (10 points) Give the asymmetric flow matrix (# trips/year). Assume 0% scrap rates. b. (30 points) Calculate the distance matrix for each distance measure: (1) Euclidean, (2) rectilinear, and (3) Tchebychev. c. (10 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?