Please, answer these two questions with typing the answers in Microsoft Word cle
ID: 3146806 • Letter: P
Question
Please, answer these two questions with typing the answers in Microsoft Word clearly, so I can understand the steps.
A regional telephone is attempting to determine the optimal location for a training facility for its operators. The operators are located in four "operations centers" and the training facility is to serve these centers. The coordinates of the four centers and the number of operators working in each are given in the table below. Table. Coordinates and number of operators in four centers Number of operators (in 1000s) 6.8 4.3 6 3.4 Town Center #1 | 32 | 58 42 Center #3 | 11 | 69 31 Center #2 | 49 Center #4 42 Q1. Solve it using the median method to determine optimal coordinates of the training facility Q2. Solve it using the gravity method to determine optimal coordinates of the training facilityExplanation / Answer
We obtain following data
Step1:
Town
x coordinates in non-decreasing order
no of operators
Cumulative no of operators
Center #3
11
6
6
Center #1
32
6.8
12.8
Center #4
42
3.4
16.2
Center #2
49
4.3
20.5
STEP:2
Since the second x co-ordinate that is center#1 in the list where cumulative weight is equals or greater than half of total weight i.e 20.5/2=12.25
So the optimal x co- ordinate is 32
STEP3:
Now we do the same process for y coordinates
Town
Y co-ordinates in non-decreasing order
no of operators
Cumulative no of operators
Center #4
31
3.4
3.4
Center #2
42
4.3
7.7
Center #1
58
6.8
14.5
Center #3
69
6
20.5
Since the third y coordinate that is center#1 in the list where cumulative weight is equals or greater than half of total weight i.e 20.5/2=12.25
So the optimal y co-ordinate is 58
Thus optimal co-ordinates are(32,58).
END
2)NOW using Gravity Method:
Town
X
Y
no of operators
Center #1
32
58
6.8
Center #2
49
42
4.3
Center #3
11
69
6
Center #4
42
31
3.4
Now from Formula of gravity method i.e
x=x.w/=w for all locations that is
x=(32*6.8+49*4.3+11*6+42*3.4)(6.8+4.3+6+3.4)
x=637.1.5
x=31.07
now y==y.w/=w for all locations that is
Y=(58*6.8+42*4.3+69*6+31*3.4)(6.8+4.3+6+3.4)
Y=53.38
So optimal co-ordinates are (31.07,53.38)
Town
x coordinates in non-decreasing order
no of operators
Cumulative no of operators
Center #3
11
6
6
Center #1
32
6.8
12.8
Center #4
42
3.4
16.2
Center #2
49
4.3
20.5