Locating a Distribution Center Northeast Parts Supply is a wholesale distributor of components for printers, fax machines, scanners, and related equipment. Northeast stocks expensive spare parts, which dealers prefer not to hold, and offers same-day delivery on any order. The firm now serves eight dealers in the New England area and wishes to locate its distribution facility at a central point. In particular, its dealers have each been assigned a location on an x-y grid, and Northeast would like to find the best location for the distribution facility.
The eight dealers and their grid locations are shown in the following table:
|
Dealer
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
x-location
y-location
|
25
32
|
82
36
|
10
71
|
27
58
|
93
68
|
14
163
|
68
149
|
147
192
|
(a) Determine the location that minimizes the sum of the distances from the distribution facility to the dealers.
(b) Determine the location that minimizes the maximum distance from the distribution facility to any of the dealers.