Timberland Inc. produces cars and has 4 plants and 6 sales depots. The data below depicts the transportation cost (of moving the car from plant to sales depot), fixed cost, and demand schedule:

Plant 1 2 3 4 5 6 Production units Fixed costs 1 80 15 30 70 40 120 40 430 2 60 85 35 10 20 60 30 300 3 20 70 20 15 30 40 50 370 4 40 30 22 30 26 100 45 180 Demand units 20 10 15 7 9 25 86/165 1280 The total production is 165 cars and the demand is 86 cars. Since production is more than demand, management wishes to shut down some plants if required.

Develop an integer optimization model to determine where to setup plants and sales depots (production and distribution system) such that cost is minimized.