Solve the comple question and explain in detail. step by step. During the war in Afghanistan, the Terrace Motor Company produced a lightweight, all$-$terrain vehicle code$-$named $"$J$99$ Terra" for the military. The company is now planning to sell the Terra to the public. It 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 C is $$32,000.$ Formulate and solve an integer programming model for this problem to assist the company in determining which plants should remain open and which should be closed and the num$$ber of vehicles that should be shipped from each plant to each warehouse to minimize total cost.