Location Section Project A small logistic company named LogTransit currently has 3 manufacturing facilities (suppliers) called Supplier #1, #2 and #3 to supply for goods of its 3 retail stores (customers) called Customer A, B, and C. Due to customer demands at stores are increasing, the company is considering to construct a new manufacturing facility. The new factory will have a supply capacity of 200 units per week. After screening many potential sites, Toledo and Cincinnati have been determined to be the two leading candidate locations for the new facility. Assume that overall Transportation costs from Suppliers to Customers will be the main determinant to determine which of the two locations to be selected as the new plant site. The following two tables provide information of i) capacity of old suppliers and new supplier candidates; ii) The per unit Transportation cost from existing Suppliers to customers and per unit Transportation cost from the new candidate supplier location to customers, and 3) demands from customers and available capacity of each supplier. Shipping cost/unit A B 10 14 10 Supplier #1 #2 Capacity 200 140 150 20 12 11 17 11 #3 12 Demand 220 220 220 Shipping cost/unit A B Capacity 200 New Supplier Toledo 18 8 14 Cincinnati 7 17 13 200 Tasks: Part I. Determine which new plant location may lead to a lower total transportation costs. You need to do the followings i) Formulate the problem into two Linear Programming models. ii) Solve each Linear Programming using Excel Solver. iii) Draw conclusion on which new site should be selected, or will have minimal transportation costs under optimal shipping schedule. Part II. Use Sensitivity Report of solver outputs for the linear programming model of Toledo" case to answer the following questions. If the shipping cost from Supplier 3 to Demand B is increased to 12, will the overall shipping quantity from Suppliers to Customers remain the same? What will be Total Transportation Cost now? ii) If the shipping cost from Supplier 3 to Demand B is increased to 20, will the optimal shipping schedule change when Toledo is select remain the same? iii) If the new Toledo capacity is increased to 210 units, how much Total Transportation costs can be reduced? iv) If the new Toledo capacity is increased to 250 units, how much Total Transportation costs can be reduced? Note Again: a) The questions should be answered using the Answer Report and Sensitivity Report from the ORIGINAL LP formulation ONLY, not from revised solution reports with LP Updated Parameters. b) Please give explanations for your answers by pointing out the exact location in the reports to support your answers