During the war with Iraq, in 1991, the Terraco Motor company produced a lightweight, all terrian 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 manucature the vehicle and four region distribution centers. The company is unsure or public demand for the Terra, so it is considering reducing its fixed operating cost by closing one or more plants, even though it would incur an increase in transportation cost. The relevant cost for the are provided in the following table. The transportation cost 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
From plant A B C D Annual production capacity Annual fixed 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.