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Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation costs and possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and is choosing between facilities with capacities of 5 or 10 million. Supply Region North America South America South Asia Europe Demand Demand Region Production and Transportation Cost per 1,000,000 Units North America 40 51 58 71 6 South South America Asia 45 51 57 47 45 51 7 63 50 4 Europe 65 60 31 53 8 Low Capacity Fixed Capacity Cost 3000 3200 2000 1800 5 5 5 5 High Capacity Fixed Cost 4500 4800 3000 2700 Capacity 10 10 10 10 Europe is critical for Future Plastic's development in the future. Hence, the company wants to ensure that either a low-capacity or a high facility capacity facility is built in the European supply region. If the high-capacity facility is built in South America, then high capacity must be built in North America as well. a. Define decision variables. Your definition must include unit size & time frame. b. Develop the Objective Function. c. Find the constraints.

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation costs and possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and is choosing between facilities with capacities of 5 or 10 million. Supply Region North America South America South Asia Europe Demand Demand Region Production and Transportation Cost per 1,000,000 Units North America 40 51 58 71 6 South South America Asia 45 51 57 47 45 51 7 63 50 4 Europe 65 60 31 53 8 Low Capacity Fixed Capacity Cost 3000 3200 2000 1800 5 5 5 5 High Capacity Fixed Cost 4500 4800 3000 2700 Capacity 10 10 10 10 Europe is critical for Future Plastic's development in the future. Hence, the company wants to ensure that either a low-capacity or a high facility capacity facility is built in the European supply region. If the high-capacity facility is built in South America, then high capacity must be built in North America as well. a. Define decision variables. Your definition must include unit size & time frame. b. Develop the Objective Function. c. Find the constraints.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation costs and possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and is choosing between facilities with capacities of 5 or 10 million. Supply Region North America South America South Asia Europe Demand Demand Region Production and Transportation Cost per 1,000,000 Units South Asia 51 47 North America 40 51 58 71 6 South America 45 57 63 50 4 45 51 7 Europe 65 60 31 53 8 Low Capacity Fixed Capacity Cost 3000 3200 2000 1800 5 5 5 5 High Capacity Fixed Cost 4500 4800 3000 2700 Capacity 10 10 10 10 Europe is critical for Future Plastic's development in the future. Hence, the company wants to ensure that either a low-capacity or a high facility capacity facility is built in the European supply region. If the high-capacity facility is built in South America, then high capacity must be built in North America as well. a. Define decision variables. Your definition must include unit size & time frame. b. Develop the Objective Function. c. Find the constraints. d. Use 'Excel - Solver' and find the optimal solution.
Transcribed Image Text:Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation costs and possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and is choosing between facilities with capacities of 5 or 10 million. Supply Region North America South America South Asia Europe Demand Demand Region Production and Transportation Cost per 1,000,000 Units South Asia 51 47 North America 40 51 58 71 6 South America 45 57 63 50 4 45 51 7 Europe 65 60 31 53 8 Low Capacity Fixed Capacity Cost 3000 3200 2000 1800 5 5 5 5 High Capacity Fixed Cost 4500 4800 3000 2700 Capacity 10 10 10 10 Europe is critical for Future Plastic's development in the future. Hence, the company wants to ensure that either a low-capacity or a high facility capacity facility is built in the European supply region. If the high-capacity facility is built in South America, then high capacity must be built in North America as well. a. Define decision variables. Your definition must include unit size & time frame. b. Develop the Objective Function. c. Find the constraints. d. Use 'Excel - Solver' and find the optimal solution.
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