A toy manufacturer produces toys in five locations throughout the country. Raw m
ID: 345101 • Letter: A
Question
A toy manufacturer produces toys in five locations throughout the country. Raw materials (primarily barrels of powdered plastic) will be shipped from a new, centralized warehouse whose location is to be determined. The monthly quantities to be shipped to each location are the same. A coordinate system has been established, and the coordinates of each location have been determined as shown. Determine the coordinates of the centralized warehouse.
location (x,y)
a 3,7
b 8,2
c 4,6
d 4,1
e 6,4
x bar =?
y bar=?
Explanation / Answer
The value of coordinates x and y for different locations are given below.
Location
x
y
Quantity (Q) (Quantities are same for each location, Assume it’s 1)
x*Q
y*Q
a
3
7
1
3
7
b
8
2
1
8
2
c
4
6
1
4
6
d
4
1
1
4
1
e
6
4
1
6
4
Total (Sum)
5
25
20
The coordinates of centralized location that will minimize distribution cost will be determined in following manner –
X-bar = ( x * Q) / Q = 25/ 5 = 5
Y-bar = ( y* Q) / Q = 20/ 5 = 4
Therefore the coordinates of the centralized warehouse is (5, 4)
Location
x
y
Quantity (Q) (Quantities are same for each location, Assume it’s 1)
x*Q
y*Q
a
3
7
1
3
7
b
8
2
1
8
2
c
4
6
1
4
6
d
4
1
1
4
1
e
6
4
1
6
4
Total (Sum)
5
25
20
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