a)
To determine: The center-of-gravity coordinates the new store to be located.
Introduction: Location is one of the important element for a business that controls the cost and expenses. Location strategies support in framing other strategies for a firm where optimal location point will provide competitive advantage to a firm.
a)

Answer to Problem 23P
The coordinates of the center of gravity are (66.69, 30.22).
Explanation of Solution
Given information:
Census Tract | Population in census tract | X,Y |
101 | 2,000 | (25, 45) |
102 | 5,000 | (25, 25) |
103 | 10,000 | (55, 45) |
104 | 7,000 | (50, 20) |
105 | 10,000 | (80, 50) |
106 | 20,000 | (70, 20) |
107 | 14,000 | (90, 25) |
Center-of-gravity coordinates of the new store:
Derive the coordinates of the Center of gravity by proceeding sequentially as per the following steps given the population data and the coordinates of various census tracts.
The various Census tracts under consideration are shown below in the graph.
The x coordinate of the centre of gravity Cx is given by the formula
where dix is the x coordinate of the location i and Qi is the shipping load to and from the location i
The y coordinate of the centre of gravity Cy is given by the formula
where diy is the y coordinate of the location i and Qi is the shipping load to and from the location i
Use equation (1) and calculate Cx as follows,
Use equation (2) and calculate Cy,
The coordinates of the center of gravity are (66.69, 30.22), marked in red color in the graph below.
Hence, the coordinates of the center of gravity are (66.69, 30.22).
b)
To determine: The change in center-of-gravity coordinates of the new store when 103 and 105 census tracts grow by 20%.
b)

Answer to Problem 23P
The new coordinates of the center of gravity marginally shifts to (66.74, 31.18).
Explanation of Solution
Given information:
Census tract 103 and 105 grow by 20%.
Census Tract | Population in census tract | X,Y |
101 | 2,000 | (25, 45) |
102 | 5,000 | (25, 25) |
103 | 12,000 | (55, 45) |
104 | 7,000 | (50, 20) |
105 | 12,000 | (80, 50) |
106 | 20,000 | (70, 20) |
107 | 14,000 | (90, 25) |
Calculation of change in center-of-gravity coordinates:
Derive the center of gravity, given that the population growth in census tracts 103 and 105 has increased by 20% as shown in the table.
Use equation (1) and calculate Cx as follows
Use equation (2) and calculate Cy
The new coordinates of the center of gravity marginally shifts to (66.74, 31.18) as shown below.
Hence, the new coordinates of the center of gravity marginally shifts to (66.74, 31.18).
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Chapter 8 Solutions
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