Mid-term-Spring-2018 ANT 510-part B Operations Management Mid-term-Spring-2018 5

Question

Mid-term-Spring-2018 ANT 510-part B Operations Management Mid-term-Spring-2018 5) A school district is considering where in town to be loc house its central office (The office must also cated 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 which school the central office should be placed to minimize the office and students. (7.5 points) center-of-gravity method to determine at average distance between the Size Location (XY (Enrollment) A (5,5) 2500 B (0,5 1000 10,000 D (5,0 2,1 4500 7500

Explanation / Answer

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

Therefore ,

Sum of enrollments in all schools x P =Sum of( X coordinate xSize of enrolment ) for 5 locations

Therefore ,

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

Or, 25500.P = 12500 + 0 + 0 + 22500 + 15000

Or, 25500.P = 50000

Or, P = 50000/ 25500

Or, P =1.96

Similarly ,

Sum of enrollments in all schools x Q =Sum of( Y coordinate xSize of enrolment ) for 5 locations

Therefore ,

( 2500 + 1000 + 10,000 + 4500 + 7500 ) x Q = 5 x 2500 + 5 x 1000 + 0 x 10,000 + 0 x 4500 + 1 x 7500

Or, 25500. Q = 25000

Or, Q = 25000/ 25500

Or, Q = 0.98

Therefore , Location coordinates of the central office will be = ( P,Q ) = ( 1.96, 0.98).

This location is nearest to the location E having coordinates ( 2, 1 )

Therefore , Central office should be placed at Location E

CENTRAL OFFICE SHOULD BE PLACED AT SCHOOLWITH LOCATION E

CENTRAL OFFICE SHOULD BE PLACED AT SCHOOLWITH LOCATION E

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