problem 5.8 (attached below). Formulate each 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 CaldoFreddo are two European manufacturers of home appliances that have merged. Hot&Cold has plants in France, Germany, and Finland, whereas CaldoFreddo 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 Tax Fixed Rate Cost Hot&Cold France 100 110 110 100 50 1,000 0.25 Germany 95 105 105 105 50 1,000 0.25 Finland 90 100 115 110 40 850 0.3 Demand 30 15 20 35 CaldoFreddo U.K. 105 120 115 90 50 1,000 0.2 Italy 110 105 85 115 60 1,150 0.35 Demand 15 20 30 20 Total Demand 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?