Future Plastics manufactures plastic products for industrial use worldwide In od
ID: 333012 • Letter: F
Question
Future Plastics manufactures plastic products for industrial use worldwide In odero meet demand, they are considerin 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 faclities with capacities of 5 or 10 million. 7. Which of these constraints will ensure that either a low capacity or a high facility capacity facility is built in the European supply region? A)Y41 + Y42 = 1 B) Y41 + Y425 I D) Y14 + Y2431 8. Which of these constraints will ensure that a low capacity facility is not built in South 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: X?? quantity shipped from supply region i to demand regionj. i-1, 2, 3, 4 andj-1.2.3.4 Y1 if facility k is selected for supply region 0 otherwise, where,2, 3,4 for each supply region; 1 (low capacity facility) or 2 (high capacity facility) A) Y12Y22 1 B) Y12 Y22-1 C) Y12+Y22-0 Production and Transportation Cost 1,000,000 Units High Capacitv 9. Detrmine the shortest route from Pearlsbrg to a the communities and farms visited by the Amcrica Amcrica Asia E Distance 65 3,000 Node Morgan Creek 2 Kitchen Cormer5 2 Kitchen Ce7Cutter's Store Morgan Creek Cedar Creek 5. The constraint for the North American supply region is: A)X1 1 +X21 + X31 + X34-5Y11-10Y21Explanation / Answer
Q5. The constraint for North American supply region is:
B) X11+X12+X13+X14 - 5Y11 - 10Y12 <= 0
X11, X12, X13, X14 represent the total supply from North American region to the four regions.
5Y11 + 10Y12 represent the supply from facilities to North American region. Total supply from North American region to the four regions must be less than the supply from the facilities to North American region.
Q6. The constraint for the South Asia demand region is:
D) X13+X23+X33+X43 = 7
LHS part of the equation represents the total supply from the four supply regions to South Asia demand region. RHS shows the demand of South Asia region, which must be exactly satisfied (not less or more).
Q7.
A) Y41+Y42 = 1
Y41 and Y42 are binary variables, so any one of them should equal to 1, such that either facility 1 or 2 is build in European region (node 4). Equal ("=") sign ensures that exactly one facility is selected.
Q8. None of the given options. The correct answer is:
Y21 = 0
numeral i=2 represents South America region and k=1 represents low capacity facility.
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