Q&A Hero

Question

Distance to COG
Project A 94
Project B 29.29
Project C 23.35
Project D 17.90

31.94(2) + 29.29(2) + 23.35(2) + 17.9(2) = 204.96 total miles traveled

Key Term: Center-of-gravity method

44) Every month, a distribution center will deliver 14,000 units to Retailer A at coordinates (20, 10), 12,000 units to Retailer B at coordinates (30, -15), and 20,000 units to Retailer C at coordinates (4, 4). Assuming no constraints on location, at what coordinates should the distribution center be located (rounded to two decimal places)?

Answer: (15.65, 0.87), where 15.65 = [20(14) + 30(12) + 4(20)]/(14 + 12 + 20), and 0.87 = [10(14) - 15(12) + 4(20)]/(14 + 12 + 20).

Key Term: Center-of-gravity method

45) A school district is considering where in town to house its central office (The office must also be located at an existing school for cost reasons). If there are five schools in the district, with locations and size given in the following table, use the center-of-gravity method to determine at which school the central office should be placed to minimize the average distance between the office and students.


Location (X,Y) Size (Enrollment)
A (5,5) 2500
B (0,5) 1000
C (0,0) 10,000
D (5,0) 4500
E (2,1) 7500

Answer: The total number of students is (2500 + 1000 + 10,000 + 4500 + 7500) = 25,500

X = [5(2500) + 0(1000) + 0(10,000) + 5(4500) + 2(7500)]/25,500 = 1.96

Y = [5(2500) + 5(1000) + 0(10,000) + 0(4500) + 1(7500)]/25,500 = .98

Rounding these gives (X,Y) of (2,1) which is closest to school E.

Key Term: Center-of-gravity method

46) A school district is considering four locations for a new high school. There are four factors the district is considering (cost of land, distance to students, land size, and traffic flow). The higher the factor score, the better. The district would like to compare results using two weighting systems. The first system would give each factor equal weight and the second would give the factors weights of .4, .2, .1, and .3 respectively. Use the factor rating method to determine which location is best for each weighting system. (Note that the weights for system 1 can be anything, as long as they're equal.)


Factor W(1) W(2) A B C D
Cost of Land 1 .4 10 20 25 5
Distance to Students 1 .2 30 25 15 20
Land Size 1 .1 5 10 20 40
Traffic Flow 1 .3 20 5 15 30

Answer: Applying the factor rating method gives the following results:

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