Make sure to identify and define the decision variables, and formulate the objective function and constraints for each problem.

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?

c. 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?

d. How should Sunchem account for the fact that exchange rates fluctuate over time?

Table 5-6 Capacity, Demand, Production, and Transportation Costs for Sunchem North Europe Japan Rest of Production South America Capacity Tons/Year America Asia Cost/Ton United $600 $1,300 $2,000 $1,200 $1,700 185 $10,000 States Germany $1,300 $600 $1,400 $1,400 $1,300 475 15,000 euro Japan $2,000 $1,400 $300 $2,100 $900 50 1,800,000 yen Brazil $1,200 $1,400 $2,100 $800 $2,100 200 13,000 real India $2,200 $1,300 $1,000 $2,300 $800 80 400,000 rupees 270 200 120 190 100 Demand (tons/year) Table 5-7 Anticipated Exchange Rates for the Next Year US$ Euro Yen Real Rupee US$ 1.000 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