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 cost and to 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 are choosing between facilities with capacities of 5 or 10 million.
The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows:
Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4.
Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility)

-Which of these constraints will ensure that a low capacity facility is not built in South America?

Question

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 cost and to 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 are choosing between facilities with capacities of 5 or 10 million.
The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows:
Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4.
Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility)

-Which of these constraints will ensure that a low capacity facility is not built in South America?

Quizplus · Accepted Answer

To ensure that a low capacity facility is not built in South America (supply region 2), we need to make sure that only the high capacity facility is selected for this region. This can be achieved by setting the sum of Y12 and Y22 equal to zero, as there can only be one facility selected for each supply region. Therefore, the correct constraint is option C: Y12 + Y22 = 0.

Future Plastics Manufactures Plastic Products for Industrial Use Worldwide