A chain of home health care firms in Louisiana needs to locate a central office from which to conduct internal audits and other periodic reviews of its facilities. These facilities are scattered throughout the state, as detailed in the following table. Each site, except for Houma, will be visited three times each year by a team of workers, who will drive from the central office to the site. Houma will be visited five times a year.
|
Map Coordinates |
||
|
City |
X |
Y |
|
Covington |
9.0 |
3.5 |
|
Donaldsonville |
7.5 |
2.5 |
|
Houma |
7.8 |
1.7 |
|
Monroe |
4.8 |
8.7 |
|
Natchitoches |
2.8 |
6.2 |
|
New Iberia |
5.3 |
2.7 |
|
Opelousas |
5.0 |
3.6 |
|
Ruston |
3.8 |
8.5 |
For the location of the new central office, the coordinates should be near:
x = __ (round your response to two decimal places).
The value of coordinates x and y for different locations are given below.
|
City |
x |
y |
Quantity (Q) (Number of visits each year) |
x*Q |
y*Q |
|
Covington |
9.0 |
3.5 |
3 |
27.0 |
10.5 |
|
Donaldsonville |
7.5 |
2.5 |
3 |
22.5 |
7.5 |
|
Houma |
7.8 |
1.7 |
5 |
39.0 |
8.5 |
|
Monroe |
4.8 |
8.7 |
3 |
14.4 |
26.1 |
|
Natchitoches |
2.8 |
6.2 |
3 |
8.4 |
18.6 |
|
New Iberia |
5.3 |
2.7 |
3 |
15.9 |
8.1 |
|
Opelousas |
5.0 |
3.6 |
3 |
15.0 |
10.8 |
|
Ruston |
3.8 |
8.5 |
3 |
11.4 |
25.5 |
|
Total (Sum) |
26 |
153.6 |
115.6 |
The coordinates of new central office that will minimize the distance will be determined in following manner –
X = (∑ x * Q) / ∑ Q = 153.6/ 26 = 5.91
Y = (∑ y* Q) / ∑ Q = 115.6/ 26 = 4.45
For the location of the new central office, the coordinates should be near
X = 5.91
Y = 4.45
Therefore the coordinates of the centralized office is (5.91, 4.45)
A chain of home health care firms in Louisiana needs to locate a central office from...