A large furniture company has six retail locations spread out across Ontario and Quebec. To better serve these retail locations, the company has decided to open new distribution centers to supply inventory to the retail locations. There are two types of costs associated with the delivery: set-up costs (fixed costs) are capital costs which may usually be written off over several years, and transportation costs which depend on the distance covered. We assume that they have been put on some comparable basis, by taking the costs over a year. There are 6 sites available for the construction of new distribution centers to deliver inventory to the retail locations. Retail Locations Distribution Center 1 2 3 4 5 6 1 100 80 50 50 60 100 2 120 90 60 70 65 100 3 140 110 80 75 130 4 160 125 100 100 80 150 5 190 150 130 6 200 180 150 Table 1: Transportation costs for satisfying entire demand of each retail location 80 oo oo o Table 1 gives the transportation costs in thousand dollars) of delivering the entire demand of each retail location from a distribution center (not the unit costs). Certain deliveries that are impossible are marked with the infinity symbol (00). The construction costs (fixed cost) for each distribution center as well as the capacity of each are listed in Table 2. Distribution Center 1 2 3 4 6 Cost (1000$) 3500 9000 10000 4000 3000 9000 Capacity (tons) 300 260 100 180 275 300 Table 2: Fixed costs and capacity limits of the distribution centers There are estimations for demand of each retail location which are shown in the following table. 4 5 6 Retail Location Demand (tons) 1 3 120 80 76 Table 3: Demand data 100 110 100 Considering that the demand of a retail location needs to be satisfied and a retail location may be delivered to from distribution centers, which distribution centers should be opened to minimize the total cost of construction and of delivery, while satisfying all demands? Formulate algebraically the corresponding model for this problem, but Do NOT solve the problem in Excel. A large furniture company has six retail locations spread out across Ontario and Quebec. To better serve these retail locations, the company has decided to open new distribution centers to supply inventory to the retail locations. There are two types of costs associated with the delivery: set-up costs (fixed costs) are capital costs which may usually be written off over several years, and transportation costs which depend on the distance covered. We assume that they have been put on some comparable basis, by taking the costs over a year. There are 6 sites available for the construction of new distribution centers to deliver inventory to the retail locations. Retail Locations Distribution Center 1 2 3 4 5 6 1 100 80 50 50 60 100 2 120 90 60 70 65 100 3 140 110 80 75 130 4 160 125 100 100 80 150 5 190 150 130 6 200 180 150 Table 1: Transportation costs for satisfying entire demand of each retail location 80 oo oo o Table 1 gives the transportation costs in thousand dollars) of delivering the entire demand of each retail location from a distribution center (not the unit costs). Certain deliveries that are impossible are marked with the infinity symbol (00). The construction costs (fixed cost) for each distribution center as well as the capacity of each are listed in Table 2. Distribution Center 1 2 3 4 6 Cost (1000$) 3500 9000 10000 4000 3000 9000 Capacity (tons) 300 260 100 180 275 300 Table 2: Fixed costs and capacity limits of the distribution centers There are estimations for demand of each retail location which are shown in the following table. 4 5 6 Retail Location Demand (tons) 1 3 120 80 76 Table 3: Demand data 100 110 100 Considering that the demand of a retail location needs to be satisfied and a retail location may be delivered to from distribution centers, which distribution centers should be opened to minimize the total cost of construction and of delivery, while satisfying all demands? Formulate algebraically the corresponding model for this problem, but Do NOT solve the problem in Excel