Problem 3: Facility Location - Center of Gravity Method (10 points) A warehouse is to be built that will support three factories. The (x.x) location of each factory, annual volume and transportation rate from each factory is given below. Use a map scaling factor of k=100 miles. Factory X Y V: Annual R: Rate ($/cwt Volume (cwt) per mile) 150,000 1.10 9.1 5.2 4.4 2.6 100,000 1.60 6.7 1.7 250,000 1.80 Factory Locations 6 8 10 a) Using the COG method, what is the optimal (.) location of a single warehouse? (5 points b) If the warehouse is located at an (x, y) of (9,1), what would be the total transportation cost? (5 points) Problem 3: Facility Location - Center of Gravity Method (10 points) A warehouse is to be built that will support three factories. The (x.x) location of each factory, annual volume and transportation rate from each factory is given below. Use a map scaling factor of k=100 miles. Factory X Y V: Annual R: Rate ($/cwt Volume (cwt) per mile) 150,000 1.10 9.1 5.2 4.4 2.6 100,000 1.60 6.7 1.7 250,000 1.80 Factory Locations 6 8 10 a) Using the COG method, what is the optimal (.) location of a single warehouse? (5 points b) If the warehouse is located at an (x, y) of (9,1), what would be the total transportation cost? (5 points)