1 PM Sat Feb 18 Home Insert Draw Layout Review View Verdana 10 B I U aAv Wittmier_MGSC369_assignment2 30. A single self-service gas station with six pumps serves a small community. A competitor is opening a new facility with 12 pumps across town. The following table shows travel times in minutes from four different areas in the community to each site and the number of customers who live in each area. Time to travel to gas station Area 1 2 3 4 six-pump station 5 1 9 15 twelve-pump station 20 8 12 6 number of customers 100 150 80 50 a. Using the Huff retail location model and assuming A = 0.2, calculate the probability of a customer traveling from each area to each site. First, calculate attraction using: Aij =S/Tij^ (17 marks) Area Six-pump station (S=1) 1 2 3 4 Aij =Sj/Tij Aij =Sj/Tij^ = 1/50.2 = 1/10.2 Aij =Sj/Tij 1/90.2 Aij =Si/Tij = 1/150.2 = 1/1.3797 = 1/1 =0.72 = 1.00 = 1/1.5518 = 0.64 = 1/1.7188 = 0.58 December 23, 2022 MGSC 369v7 Assignment 2 Athabasca University Twelve-pump station Aij =Sj/Tij^ (S=2) Aij =Sj/Tij^ Aij =Si/Tij^ = 2/200.2 Aij =Sj/Tij = 2/80.2 = 2/120.2 = 2/60.2 = 2/1.8206 = 2/1.5157 = 1.10 Aji 1.82 = 1.32 2.32 = 2/1.6438 = 1.22 1.86 Second, calculate probability using: Pij = Aij/>Aij = 2/1.4310 = 1.40 1.98 Area Six-pump station (S=1) 1 2 3 Pij = Aij/Aij Pij = Aij/Aij Pij = Aij/Aij = 0.72/1.82 = 0.40 = 1.00/2.32 = 0.64/1.86 = 0.43 = 0.34 Twelve-pump station |Pij = Aij/Aij (S=2) = 1.10/1.82 = 0.60 Pij = Aij/Aij = 1.32/2.32 = 0.57 Pij = Aij/Aij = 1.22/1.86 = 0.66 4 Pij = Aij/Aij = 0.58/1.98 = 0.29 Pij = Aij/Aij = 1.40/1.98 = 0.71 b. ili Estimate the proportion of the existing market that the six-pump station will lose to the new competitor. (10 marks) > 66%