Problem:
Spearmint Gum Manufacturing is a manufacturer of recycled gum. Its products are enjoying a growing reputation and increased demand throughout North America because of its unique texture and natural flavors. Spearmint is considering a new plant in Alaska to service the entire state's home rule cities. A key concern in its search for a new location is the resultant transportation costs to serve its key markets. Following is a list of home rule cities where its main wholesale customers are located, along with estimated annual demand in cases of product for each.
|
City
|
X-Coordinate
|
Y-Coordinate
|
# Cases of Gum
|
|
Anchorage
|
1200
|
725
|
52,000
|
|
Fairbanks
|
800
|
450
|
28,000
|
|
Juneau
|
600
|
650
|
16,000
|
|
Sitka
|
300
|
320
|
14,000
|
|
Ketchikan
|
1400
|
900
|
8,000
|
|
Kenai
|
700
|
500
|
11,000
|
|
Kodiak
|
250
|
250
|
12,000
|
|
Palmer
|
675
|
400
|
7,000
|
|
Valdez
|
850
|
520
|
15,000
|
|
Petersburg
|
375
|
470
|
6,000
|
|
Seward
|
275
|
300
|
1,500
|
|
Wrangell
|
426
|
700
|
1,000
|
|
Cordova
|
350
|
125
|
875
|
|
North Pole
|
2300
|
1250
|
469
|
|
Nenana
|
470
|
180
|
3,000
|
Required:
Question 1) Use the centroid method to recommend a location for the new gum plant. Round your coordinates to one decimal place.
Spearmint Gum Manufacturing realizes that it may be too ambitious to service all Alaska's home rule cities so it decides to limit its geographic service area to include the following cities.
|
City
|
X-Coordinate
|
Y-Coordinate
|
# Cases of Gum
|
|
Anchorage
|
1200
|
725
|
52,000
|
|
Fairbanks
|
800
|
450
|
28,000
|
|
Juneau
|
600
|
650
|
16,000
|
|
Valdez
|
850
|
520
|
15,000
|
|
Sitka
|
300
|
320
|
14,000
|
|
Kodiak
|
250
|
250
|
12,000
|
Question 2) Use the centroid method to recommend a location for the new gum plant. Round your coordinates to one decimal place.
Solve the given numerical problem and illustrate step by step calculation.