PGL, 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 where the plant is located. The major markets for the inks are North America, South America, Europe, Japan 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. Table 1. Capacity, Demand, Production and Transportation Costs for PGL Variable production and shipping costs Plant Production Capacity North South Europe Japan America America Asia (Tons/Year) Cost/Ton United $600 $1300 States $2000 $1200 $1700 185 $10000 Germany $1300 $600 $1400 $1400 $1300 475 15000 Euro Japan $2000 $1400 $300 1800000 $2100 $900 50 Yen Brazil $1200 $1400 $2100 $800 $2100 200 13000 Real 400000 India $2200 $1300 $1000 $2300 $800 80 Rupees Demand 270 200 120 (tons/year) 100 190 1 Table 2. Anticipated Exchange Rates for the Next Year US $ Euro Yen Real Rupee US $ 1 1.993 | 107.7 1.78 43.55 Euro 0.502 1 54.07 0.89 21.83 Yen 0.0093 0.0185 1 0.016 0.405 Real 0.562 1.124 60.65 1 24.52 Rupee 0.023 0.046 2.47 0.041 1 a) If there are no limits on the amount produced in a plant, how much should each plant produce? What will be the shipping plan? What will be the optimal total cost? Assume the exchange rates are expected as in Table 2. b) If no plant can run below 80% of the capacity, how much should each plant produce? What will be the shipping plan? What will be the optimal total cost? Assume the exchange rates are expected as in Table 2. c) Can adding 10 tons of capacity in any plant reduce costs? PGL, 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 where the plant is located. The major markets for the inks are North America, South America, Europe, Japan 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. Table 1. Capacity, Demand, Production and Transportation Costs for PGL Variable production and shipping costs Plant Production Capacity North South Europe Japan America America Asia (Tons/Year) Cost/Ton United $600 $1300 States $2000 $1200 $1700 185 $10000 Germany $1300 $600 $1400 $1400 $1300 475 15000 Euro Japan $2000 $1400 $300 1800000 $2100 $900 50 Yen Brazil $1200 $1400 $2100 $800 $2100 200 13000 Real 400000 India $2200 $1300 $1000 $2300 $800 80 Rupees Demand 270 200 120 (tons/year) 100 190 1 Table 2. Anticipated Exchange Rates for the Next Year US $ Euro Yen Real Rupee US $ 1 1.993 | 107.7 1.78 43.55 Euro 0.502 1 54.07 0.89 21.83 Yen 0.0093 0.0185 1 0.016 0.405 Real 0.562 1.124 60.65 1 24.52 Rupee 0.023 0.046 2.47 0.041 1 a) If there are no limits on the amount produced in a plant, how much should each plant produce? What will be the shipping plan? What will be the optimal total cost? Assume the exchange rates are expected as in Table 2. b) If no plant can run below 80% of the capacity, how much should each plant produce? What will be the shipping plan? What will be the optimal total cost? Assume the exchange rates are expected as in Table 2. c) Can adding 10 tons of capacity in any plant reduce costs