The Terraco Motor Company has produced a lightweight, all-terrain vehicle code-named “J99 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.

Transportation Costs ($1,000s) to Warehouse Annual Production Capacity Annual Fixed From Plant A B C D Operating Costs 1 $56 $21 $32 $65 12,000 $2,100,000 2 18 46 7 35 18,000 850,000 3 12 71 41 52 14,000 1,800,000 4 30 24 61 28 10,000 1,100,000 5 45 50 26 31 16,000 900,000 Annual Demand 6,000 14,000 8,000 10,000 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 number of vehicles that should be shipped from each plant to each warehouse to minimize total cost.