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 Peoria Decatur Joliet COORDINATES (x, y) 308, 299 366, 469 475, 181 C₂ Cy VOLUME (PARTS PER YEAR) 3,900 5,900 2,850 Use the centroid method to determine the best location for this new facility. (Round your answers to 1 decimal place.)

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Can you assist me with homework chapter 15 question 6. I am having a difficult time with the calculations on the excel spreadsheet. Thank you. 

### Determining the Optimal Location for a New Manufacturing Facility

A small manufacturing facility is being planned to supply parts to three major manufacturing facilities. The table below provides the coordinates of the existing plants along with their volume requirements in parts per year:

#### Plant Data

| Plant Location | Coordinates (x, y) | Volume (Parts per Year) |
|----------------|--------------------|--------------------------|
| Peoria         | (388, 299)         | 3,900                    |
| Decatur        | (366, 469)         | 5,900                    |
| Joliet         | (475, 181)         | 2,850                    |

### Objective

**Task**: Use the centroid method to determine the best location for this new facility. 

**Instructions**: Calculate the centroid coordinates (Cx, Cy) based on the data provided. **Round your answers to one decimal place.**

| Centroid Coordinates | Value        |
|----------------------|--------------|
| C<sub>x</sub>        | \_\_\_\_\_\_ |
| C<sub>y</sub>        | \_\_\_\_\_\_ |

### Centroid Method Explanation

The centroid method helps in finding an optimal location by balancing the locations and demands (volumes) of the existing facilities. It involves finding the weighted average of the coordinates based on their volume requirements.
Transcribed Image Text:### Determining the Optimal Location for a New Manufacturing Facility A small manufacturing facility is being planned to supply parts to three major manufacturing facilities. The table below provides the coordinates of the existing plants along with their volume requirements in parts per year: #### Plant Data | Plant Location | Coordinates (x, y) | Volume (Parts per Year) | |----------------|--------------------|--------------------------| | Peoria | (388, 299) | 3,900 | | Decatur | (366, 469) | 5,900 | | Joliet | (475, 181) | 2,850 | ### Objective **Task**: Use the centroid method to determine the best location for this new facility. **Instructions**: Calculate the centroid coordinates (Cx, Cy) based on the data provided. **Round your answers to one decimal place.** | Centroid Coordinates | Value | |----------------------|--------------| | C<sub>x</sub> | \_\_\_\_\_\_ | | C<sub>y</sub> | \_\_\_\_\_\_ | ### Centroid Method Explanation The centroid method helps in finding an optimal location by balancing the locations and demands (volumes) of the existing facilities. It involves finding the weighted average of the coordinates based on their volume requirements.
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