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 Upper A ​(6​,11​) 5 Upper B ​(5​,8​) 10 Upper C ​(4​,8​) 14 Upper D ​(7​,5​) 6 Upper E ​(8​,8​) 14 Upper F ​(3​,1​) 11 Upper G ​(3​,6​) 4 ​a) For the location of the proposed new central​ hub, the coordinates should be​ near: x​ = 5.23 ​(round your response to two decimal​ places). y​ = 6.64 ​(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​ = nothing ​(round your response to two decimal​ places).

Answer 1

(a)

City - j	Xj	Yj	Lj	Xj.Lj	Yj.Lj
A	6	11	5	30	55
B	5	8	10	50	80
C	4	8	14	56	112
D	7	5	6	42	30
E	8	8	14	112	112
F	3	1	11	33	11
G	3	6	4	12	24
Totals			64	335	424
Centroid
Cx	335/64 =	5.23
Cy	424/64 =	6.63

(b)

City - j	Xj	Yj	Lj	Xj.Lj	Yj.Lj
A	6	11	10	60	110
B	5	8	10	50	80
C	4	8	14	56	112
D	7	5	6	42	30
E	8	8	14	112	112
F	3	1	11	33	11
G	3	6	4	12	24
Totals			69	365	479
Centroid
Cx	365/69 =	5.29
Cy	479/69 =	6.94