35) A school district is considering where in town to house its central office (

Question

35) 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. (4 pts.) Size Location (X,Y (Enrollment) (0.5)1000 10,000 4500 7500 5,0 36) Geographic information systems can assist the location decision by: (2 pts.) A) automating center-of-gravity problems. B) computerizing factor-rating analysis. C) combining geography with demographic analysis. D) updating transportation method solutions. E) providing good Internet placement for virtual storefronts.

Explanation / Answer

Answer to Question 35 :

Let the location of central office = ( P , Q )

As per center of gravity method ,

Sum of enrollment size x P = Sum of ( X axis x Enrollment size ) five locations

Or, ( 2500 + 1000 + 10,000 + 4500 + 7500 ) x P = 5 x 2500 + 0 x 1000 + 0 x 10000 + 5 x 4500 + 2 x 7500

Or, 25500.P = 12500 + 22500 + 15000

Or 25500.P = 50,000

Or, P = 50,000/25500

Or, P = 1.96

Similarly ,

Sum of enrollment size x P = Sum of ( Y axis x Enrollment size ) five locations

Or, ( 2500 + 1000 + 10,000 + 4500 + 7500 ) x P = 5 x 2500 + 5 x 1000 + 0 x 10000 + 0 x 4500 + 1 x 7500

Or, 25500.Q = 12500 + 5000 + 7500

Or, 25500.Q = 25000

Or, Q = 25000/25500

Or, Q = 0.98

Thus the location of central office should be ( 1.96, 0.98 ) which is closest to location E ( 2,1 )

CENTRAL OFFICE SHOULD BE PLACED AT LOCATION E

CENTRAL OFFICE SHOULD BE PLACED AT LOCATION E

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