Q.15-10OQ Question:聽A small manufacturing... [FREE SOLUTION]

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Operations And Supply Chain Management

F. Robert Jacobs

Business Studies

14th Edition 路 800 pages

ISBN: 9780078024023

Chapter 3: Q.15-10OQ (page 395)

Question:A small manufacturing facility is being planned that will feed parts to three heavy manufacturing facilities. The locations of the current plants with their coordinates and volume requirements are given in the following table:
Plant Location
Coordinates (x,y)
Volume (parts per year)
Peoria
300,320
4,000
Decatur
375,470
6,000
Joliet
470,180
3,000
Use the centroid method to determine a location for this new facility.

Short Answer

Expert verified

Answer

The new warehouse would be located at (373.84,356.92).

Step by step solution

Formula to calculate the coordinates

$C_{x} = \frac{\underset{}{鈭�} X_{i} Y_{i}}{\underset{}{鈭�} V_{i}}, C_{y} = \frac{\underset{}{鈭�} Y_{i} V i}{\underset{}{鈭�} V_{i}},$

Prepare the chart to get the coordinates

The chart is shown below:

Put the calculated values in the above formula

$C_{x i} = \frac{4860000}{13000} = 373.84$

X coordinate is 373.84.

$C_{y i} = \frac{4640000}{13000} = 356.92$

Y coordinate is 356.92.

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New York	50000
Fort Worth	70000
San Diego	60000
Minneapolis	80000

Boulder	100000
Macon	100000
Gary	150000

Produced at	New York	Fort Worth	San Diego	Minneapolis
Boulder	7	11	8	13
Macon	20	17	12	10
Gary	8	18	13	16

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Short Answer

Step by step solution

Formula to calculate the coordinates

Prepare the chart to get the coordinates

Put the calculated values in the above formula

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Plant Location	Coordinates (x,y)	Volume (parts per year)
Peoria	300,320	4,000
Decatur	375,470	6,000
Joliet	470,180	3,000