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)

-The constraint for the North American supply region is:
A) X11 + X21 + X31 + X34 - 5Y11 - 10Y21 ≤ 0
B) X11 + X12 + X13 + X14 - 5Y11 - 10Y12 ≤ 0
C) X11 + X12 + X13 + X14 - 3200Y11 - 4800Y12 ≤ 0
D) X11 + X12 + X13 + X14 - 5Y11 - 10Y12 = 0

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)
 
-The constraint for the North American supply region is:
A) X11 + X21 + X31 + X34 - 5Y11 - 10Y21 ≤ 0 
B) X11 + X12 + X13 + X14 - 5Y11 - 10Y12 ≤ 0 
C) X11 + X12 + X13 + X14 - 3200Y11 - 4800Y12 ≤ 0 
D) X11 + X12 + X13 + X14 - 5Y11 - 10Y12 = 0

Quizplus · Accepted Answer

The correct constraint for the North American supply region likely involves variables representing the quantities shipped from North America to various destinations (X11, X12, X13, X14) and variables representing the capacities or other constraints related to shipping or production (Y11, Y12). Option B is the only one that correctly sums all shipments from North America to different regions (X11, X12, X13, X14) and subtracts terms that likely represent capacity or cost constraints multiplied by some factors (5Y11, 10Y12), making it a plausible constraint for managing supply from North America.

Future Plastics Manufactures Plastic Products for Industrial Use Worldwide