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Question 3 20 pts During the war in Afghanistan the Terraco Motor Company produced a lightweight, all-terrain vehicle codenamed J99 Terra" for the military. The company is now planning to sell the Terra to the publicit has five plants that manufacture the vehicle and four regional distribution centers. The company is unsure of public demand for the Terra, so it is considering reducing its fixed operating costs by closing one or more plants, even though it would incur an increase in transportation costs. The relevant costs for the problem are provided in the following table. The transportation costs are per thousand vehicles shipped for example, the cost of shipping 1,000 vehicles from plant 1 to warehouse is $32,000. Transportation Costs (51.000s to Warehouse Annual Annual Fixed From B c D Production Operating Capacity Costs 1 56 21 32 65 12000 2100000 2 18 46 7 35 18000 850000 3 12 71 41 52 14000 1800000 4 30 24 61 29 10000 1100000 5 45 50 26 31 16000 900000 Annual 6000 Demand 14000 8000 10000 al Formulate and solve an integer programming model for this problem to assist the company in determining which plants should remain open and which should be closed and the number of vehicles that should be shipped from each plant to each warehouse to minimize total cost. (The model should be written symbolically and be solved by Excell