A mattress manufacturer produces mattresses in 5 locations in the North America. The company isplanning a new production plant which will supply box springs to all 5 mattress plants. The mattressplants have been located on a coordinate system as follows:Mattress PlantCoordinates (X,Y)A7,2В4,55,4D6,1E8,3Suppose shipments of box springs to each plant per week were the following: plant A 200 units; plant B400 units; plant C 300 units; plant D 400 units; plant E 100 units. Which of the following is the closestto the optimal location for the box spring plant?O A. 7.7,4.3O B. 5.5,3.1O C. 4.3,7.7O D. 3.1,4.3OE. 3.1,5.5

Optimal location: The optimal location is the location that will be nearest to all 5 plants and will cost the least. It is calculated on the basis of the coordinates of all five plants. It involves applying suitable quantitative models to the current logistics systems and alternative systems to find the optimal locations.Determine the optimal location of the X and Y coordinate by multiplying the X and Y by the shipment charges: Plant X Y Shipment (W) X×W Y×W A 7 2 200 1,400 400 B 4 5 400 1,600 2,000 C 5 4 300 1,500 1,200 D 6 1 400 2,400 400 E 8 3 100 800 300 Total 1,400 7,700 4,300 Optimal Location (X Coordinate)=ΣXWΣW=7,7001,400=5.5 Optimal Location (Y Coordinate)=ΣYWΣW=4,3001,400=3.1 Hence, the optimal location of the X and Y coordinates is 5.5 and 3.1The optimal location of the X and Y coordinates is 5.5,3.1 and not 7.7,4.3. So, option A is incorrect. The optimal location of the X and Y coordinates is 5.5,3.1 and not 4.3,7.7. So, option C is incorrect. The optimal location of the Y coordinates is 3.1 and not for the X coordinate. So, options D and E are incorrect. Therefore, the correct option is B.