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Make sure to identify and define the decision variables, and formulate the objective function and constraints for each problem. You may use Excel to solve the mathematical problems. 1. (15 points) Sunchem, a manufacturer of printing inks, has five manufacturing plants worldwide. Their locations and capacities are shown in Table 1 along with the cost of producing 1 ton of ink at each facility. The production costs are in the local currency of the country that where the plant is located. The major markets for the inks are North America, Europe, Japan, South America, and the rest of Asia. Demand at each market is shown in Table 1. Transportation costs from each plant to each market in U.S. dollars are shown in Table 1. Management must come up with a production plan for the next year. a. If exchange rates are expected as in Table 2, and no plant can run below 50 percent capacity, how much should each plant produce and which markets should each plant supply? b. If there are no limits on the minimum amount produced in a plant, how much should each plant produce? Can adding 10 tons of capacity in any plant reduce costs? d. How should Sunchem account for the fact that exchange rates fluctuate over time? C. Transportation costs from each plant to each market in U.S. Dollars N. America S. America Europe Rest of Asia Capacity (ton/yr) Japan Production Cost per Ton US 600 1,200 1,300 2,000 1,700 185 $ 10,000 Germany 1,300 1,400 600 1,400 1,300 475 Euro 15,000 Japan 2,000 2,100 1,400 300 900 50 Yen 180,000 Brazil 1,200 800 1,400 2,100 2,100 210 Real 13,000 2,200 2,300 1,300 1,000 800 80 Rs. 400,000 India Demand (ton/yr) 270 190 200 120 100 Table 2. Anticipated Exchange Rates for the Next Year Real 1.78 0.89 US$ Euro Yen Real Rupee US$ 1 .502 0.0093 0.562 0.023 Euro 1.993 1 0.0185 1.124 0.046 Yen 107.7 54.07 1 60.65 2.47 Rupee 43.55 21.83 0.405 24.52 1 0.016 1 0.041