I need decision variables, constraints, and integer linear program. No need to actually solve.

Two Additional Constraints: Plant 3 must not open if Plant 1 is open. Plant 5 opens only if its production level is at least half of its full capacity.

During the war with Iraq in 1991, the Terraco Motor Company 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 ($1,000) to Warehouse Annual Production Capacity Annual Fixed Operating Cost B $21 46 From Plant 1 2. 3 4 5 Annual Demand A $56 18 12 30 45 6,000 71 Nmin $32 7 41 61 26 8,000 D $65 35 52 28 31 10,000 12,000 18,000 14,000 10,000 16,000 $2,100,000 850,000 1,800,000 1,100,000 900,000 24 50 14,000