Problem 1 (45 points): This problem is a combination of binary integer programming and transportation problem A firm has six sales centers in Quebec and has decided to open new warehouses to deliver its goods from the warehouses to the sales centers. 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 5 sites available for the construction of new warehouses to deliver goods to the six sales centers. The following table (Table 1) gives the transportation costs (in thousand dollars) of delivering the entire demand of each sales center from a warehouse (not the unit costs). Certain deliveries that are impossible are marked with the infinity symbol (co).Sales Centers Warehouse 2 100 80 50 50 60 100 120 90 60 70 65 140 120 80 80 175 130 160 125 100 100 150 190 150 130 DO Table 1: Transportation costs (in $1000) for satisfying entire demand of each sales center The construction costs (fixed cost) for each warehouse as well as the capacity of each warehouse are listed in Table 2. Warehouse 2 5 Cost ($1000) 4000 9000 10000 5000 9000 Capacity(tons) 280 250 100 180 250 Table 2: Fixed costs (in $1000) and capacity limits of the warehouse locations There are estimations for demand of each sales center which are shown in Table 3. Sales center 2 3 4 5 6 Demand (tons) 150 90 80 160 100 200 Table 3: Demand dataConsidering that the demand of a sales center needs to be satised and asides center may be delivered to from several Warehouses. a. Formulate algebraically the corresponding model that will determine which warehouses should he opened to minimiZe the total cost of cons traction and of deli'Very, while satisfying all demands. Dene the decision variables, objectiVe function, and constraints (25 points) b. Formulate this problem on a spreadsheet and use Excel's Solver to determine which warehouse the rm should operate and how goods should be distributed from each warehouse to each sales center to minimize the total cost. (Provide the corresponding \"Excel Spreadsheet\" and the \"Answer Report?) Include \"managerial statements\" that communicate the results of the analyses (i.e. describe verbally the results). (20 points)