2. [30 Pt.] [DO NOT USE EXCEL TO SOLVE THIS PROBLEM.) (SHOW FORMULATIONS BELOW by ANSWERING al, a2 and a3. During the war with Iraq in 1991, the Terraco Motor Company produced a lightweight, allterrain 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 I to warehouse C is $32,000. $21 $32 Transportation Costs ($1,000s) to Warehouse From Plant B C. D 1 556 $65 2 18 46 7 35 3 12 71 41 52 30 24 28 45 50 26 31 Annual Demand 6,000 14,000 8.000 10,000 Annual Production Capacity 12,000 18,000 14,000 10,000 16,000 Annual Fixed Operating costs $2,100,000 850,000 1,800,000 1,100,000 900,000 61 (a) Formulate 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. al) [5] Define decision variables a2) [10] Define objective function 3) [15] Define the constraints