Question

The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub.

                                                                                                 

City	Map Coordinates ​(​x,y​)	Shipping Load
A	​(6,10)	4
B	​(6​,7​)	9
C	​(3​,9)	16
D	​(7,4)	5
E	​(6,9​)	15
F	​(4,2​)	10
G	​(2​,7​)	6

​a) For the location of the proposed new central​ hub, the coordinates should be​ near:

x​ = ____ ​(round your response to two decimal​ places).

y​ = _____ ​(round your response to two decimal​ places).

​b) If the shipments from city A double​, for the location of the proposed new central​ hub, the coordinates should be​ near:

x​ = ___ ​(round your response to two decimal​ places).

y​ = ___ ​(round your response to two decimal​ places).

Answer 1

CITY	LOCATION X	LOCATION Y	LOAD
1	6	10	4
2	6	7	9
3	3	9	16
4	7	4	5
5	6	9	15
6	4	2	10
7	2	7	6

X BAR = SIGMA(Xi * Vi) / SIGMA(Vi)

(6*4) + (6*9) + (3*16) + (7*5) + (6*15) + (4*10) + (2*6) / (4 + 9 + 16 + 5 + 15 + 10 + 6) = 4.66

Y BAR = SIGMA(Yi * Vi) / SIGMA(Vi)

(10*4) + (7*9) + (9*16) + (4*5) + (9*15) + (2*10) + (7*6) / (4 + 9 + 16 + 5 + 15 + 10 + 6) = 7.14

LOCATION = XBAR, YBAR = 4.66, 7.14

2.

CITY	LOCATION X	LOCATION Y	LOAD
1	6	10	8
2	6	7	9
3	3	9	16
4	7	4	5
5	6	9	15
6	4	2	10
7	2	7	6

X BAR = SIGMA(Xi * Vi) / SIGMA(Vi)

(6*8) + (6*9) + (3*16) + (7*5) + (6*15) + (4*10) + (2*6) / (8 + 9 + 16 + 5 + 15 + 10 + 6) = 4.74

Y BAR = SIGMA(Yi * Vi) / SIGMA(Vi)

(10*8) + (7*9) + (9*16) + (4*5) + (9*15) + (2*10) + (7*6) / (8 + 9 + 16 + 5 + 15 + 10 + 6) = 7.3

LOCATION = XBAR, YBAR = 4.74, 7.3