QUESTION 1: Company A wants to determine the locations of its distribution centers. The operating costs of distribution centers have a piecewise linear structure and the annual fixed cost (fi) for each center is $100.000 and the variable cost (gi) is $4 per unit. Facilities cannot be operated economically for activity levels below 5000 units and above 25000 units per year. The distances between the company's potential distribution centers and sales regions and the demands of sales regions are given in the table below. Transportation is carried out by trucks with a capacity of 1000 units whose cost is equal to $0.75 per kilometer. The company is able to locate a maximum of 2 distribution centers. Construct the mixed integer programming model that determines where the facilities will be located in order to minimize the total cost. (30p) QUESTION 1: Company A wants to determine the locations of its distribution centers. The operating costs of distribution centers have a piecewise linear structure and the annual fixed cost (fi) for each center is $100.000 and the variable cost (gi) is $4 per unit. Facilities cannot be operated economically for activity levels below 5000 units and above 25000 units per year. The distances between the company's potential distribution centers and sales regions and the demands of sales regions are given in the table below. Transportation is carried out by trucks with a capacity of 1000 units whose cost is equal to $0.75 per kilometer. The company is able to locate a maximum of 2 distribution centers. Construct the mixed integer programming model that determines where the facilities will be located in order to minimize the total cost. (30p)