Question

Question 7 - Solve the following case (pg. 300 of the text book).

(5 marks)

Acadian Bakers

Acadian Bakers is a small but well known bakery, making and selling cakes and croissants in Houston. Its major customers, their locations on a coordinate system, and their weekly purchases are listed below. Acadian’s coordinates are (27, 36).

Coordinates
Customer	X	Y	Weekly Purchases ($)
B. Catering	22	31	80
B. Bar & Grill	38	38	70
H’s	38	36	90
H Club	38	37	120
H.C. Club	30	33	90
J’s Hideaway	−10	12	60
M’s	38	36	140
M. Club	−10	44	140
N.M.	47	33	300
K.S. Catering	33	33	50

Is Acadian centrally located to serve its customers?

Answer 1

	Customer	X	Y	Weekly Purchases ($) (l)	lx	ly
	B. Catering	22	31	80	1760	2480
	B. Bar & Grill	38	38	70	2660	2660
	H’s	38	36	90	3420	3240
	H Club	38	37	120	4560	4440
	H.C. Club	30	33	90	2700	2970
	J’s Hideaway	-10	12	60	-600	720
	M’s	38	36	140	5320	5040
	M. Club	-10	44	140	-1400	6160
	N.M.	47	33	300	14100	9900
	K.S. Catering	33	33	50	1650	1650
Total				1140	34170	39260

Center of gravity: x-coordinate = sum (lx)/sum(l) = 34170/1140= 29.97

y-coordinate =sum (ly)/sum(l) = 39260/1140 = 34.44

So Acadian’s coordinates should have been (29.97,34.44) to be located centrally which is not the case here so Acadian is not centrally located