A manufacturer of oak barrels has factories in an area at the location coordinates provided in the following table. Each coordinate unit represents approximately 10 miles. The yearly demand at each factory is also given.
| Factory |
Demand |
X-Coordinate |
Y-Coordinate |
| Manchester |
14,000 |
80 |
60 |
| Fayetteville |
17,000 |
60 |
10 |
| Columbia |
5,000 |
30 |
90 |
| Lawrenceburg |
3,000 |
30 |
20 |
Management has decided to build a new factory to supply raw material to these factories. The location of the new factory should be central to the existing factories.
Respond to the following in a Microsoft Excel worksheet:
- What should be the map coordinates of the new factory? Graph the locations of the four factories and the proposed raw material factory.
- Is the location of the proposed raw material factory where you expected it to be based on the coordinates of the other factories? Why or why not?
- What is the main contributing factor leading to the location of the proposed raw material factory?
Support your responses with examples.