problem 5.8 (attached below). Formulate cach scenario using mathematical programming (optimization). Use excel solver to find the optimum solutions to scenarios. Submit both your mathematical models and excel file. Hot&Cold and Caldo Freddo are two European manufacturers of home appliances that have merged. Hot&Cold has plants in France, Germany, and Finland, whereas Caldo Freddo has plants in the United Kingdom and Italy. The European market is divided into four regions: north, east, west, and south. Plant capacities (millions of units per year), annual fixed costs (millions of euros per year), regional demand (millions of units), and variable production and shipping costs (euros per unit) are as shown in the table: Variable Production and Shipping Costs North East South West Capacity Annual Fixed Cost Tax Rate 100 SO 0.25 50 95 90 1,000 1,000 850 110 105 115 20 TIS 0.25 0.3 40 Hot&Cold France Germany Finland Demand Caldo Freddo U.K. Italy Demand Total Demand 110 105 100 15 120 105 20 30 100 105 110 35 90 113 105 50 85 1,000 1,150 110 15 0.2 0.35 60 30 20 45 35 50 55 Each appliance sells for an average price of 300 euros. All plants are currently treated as profit centers, and the company pays taxes separately for each plant. Tax rates in the various countries are as follows: France, 0.25, Germany, 0.25; -Finland, 0.3; UK, 0.2; and Italy, 0.35. a) Before the merger, what is the optimal network for each of the two firms if their goal is to minimize costs? What is the optimal network if the goal is to maximize after-tax profits? b) After the merger, what is the minimum cost configuration if none of the plants is shut down? What is the configuration that maximizes after-tax profits if none of the plants is shut down? c) After the merger, what is the minimum cost configuration if plants can be shut down (assume that a shutdown saves 100 percent of the annual fixed cost of the plant)? What is the configuration that maximizes after-tax profits? problem 5.8 (attached below). Formulate cach scenario using mathematical programming (optimization). Use excel solver to find the optimum solutions to scenarios. Submit both your mathematical models and excel file. Hot&Cold and Caldo Freddo are two European manufacturers of home appliances that have merged. Hot&Cold has plants in France, Germany, and Finland, whereas Caldo Freddo has plants in the United Kingdom and Italy. The European market is divided into four regions: north, east, west, and south. Plant capacities (millions of units per year), annual fixed costs (millions of euros per year), regional demand (millions of units), and variable production and shipping costs (euros per unit) are as shown in the table: Variable Production and Shipping Costs North East South West Capacity Annual Fixed Cost Tax Rate 100 SO 0.25 50 95 90 1,000 1,000 850 110 105 115 20 TIS 0.25 0.3 40 Hot&Cold France Germany Finland Demand Caldo Freddo U.K. Italy Demand Total Demand 110 105 100 15 120 105 20 30 100 105 110 35 90 113 105 50 85 1,000 1,150 110 15 0.2 0.35 60 30 20 45 35 50 55 Each appliance sells for an average price of 300 euros. All plants are currently treated as profit centers, and the company pays taxes separately for each plant. Tax rates in the various countries are as follows: France, 0.25, Germany, 0.25; -Finland, 0.3; UK, 0.2; and Italy, 0.35. a) Before the merger, what is the optimal network for each of the two firms if their goal is to minimize costs? What is the optimal network if the goal is to maximize after-tax profits? b) After the merger, what is the minimum cost configuration if none of the plants is shut down? What is the configuration that maximizes after-tax profits if none of the plants is shut down? c) After the merger, what is the minimum cost configuration if plants can be shut down (assume that a shutdown saves 100 percent of the annual fixed cost of the plant)? What is the configuration that maximizes after-tax profits