Table 13.6
Union Fork, Inc. has five distribution centers located at the location coordinates given as follows. The demand at each center is also given.

-Use the information in Table 13.6. What is the total load-distance score for the two plants if Plant 1 is located at the center of gravity serving A, B, and C, and Plant 2 is at the center of gravity serving D and E? (Assume Euclidean, or straight line, distance.)
A) less than or equal to 240
B) more than 240 but less than or equal to 260
C) more than 260 but less than or equal to 280
D) more than 280

Question

Table 13.6
Union Fork, Inc. has five distribution centers located at the location coordinates given as follows. The demand at each center is also given.
 
-Use the information in Table 13.6. What is the total load-distance score for the two plants if Plant 1 is located at the center of gravity serving A, B, and C, and Plant 2 is at the center of gravity serving D and E? (Assume Euclidean, or straight line, distance.)
A) less than or equal to 240 
B) more than 240 but less than or equal to 260 
C) more than 260 but less than or equal to 280 
D) more than 280

Quizplus · Accepted Answer

First, we need to find the center of gravity for each group of distribution centers:

Center of gravity for A, B, and C:

x-coordinate = [5(2) + 3(5) + 2(3)] / (5 + 3 + 2) = 3.33
y-coordinate = [5(3) + 3(4) + 2(6)] / (5 + 3 + 2) = 3.77

Center of gravity for D and E:

x-coordinate = [2(8) + 3(6)] / (2 + 3) = 6.2
y-coordinate = [2(5) + 3(8)] / (2 + 3) = 7.3

Using the distance formula, we can calculate the distance from each distribution center to each plant location:

Total load-distance score for Plant 1:

3.16(5) + 2.24(12) + 2.91(8) + 2.88(7) + 1.12(12) = 68.08

Total load-distance score for Plant 2:

4.47(6) + 4.12(2) = 26.54

Therefore, the total load-distance score for the two plants is 68.08 + 26.54 = 94.62, which is more than 260 but less than or equal to 280. The answer is C.

Table 13.6 Union Fork, Inc. Has Five Distribution Centers Located at the at the Location