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 distribution centers A, B, and C, and Plant 2 is located at the center of gravity serving D and E? (Assume rectilinear distance.)
A) less than or equal to 300
B) more than 300 but less than or equal to 350
C) more than 350 but less than or equal to 400
D) more than 400

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 distribution centers A, B, and C, and Plant 2 is located at the center of gravity serving D and E? (Assume rectilinear distance.)
A) less than or equal to 300 
B) more than 300 but less than or equal to 350 
C) more than 350 but less than or equal to 400 
D) more than 400

Quizplus · Accepted Answer

First, we need to calculate the center of gravity for the three distribution centers A, B, and C:

X-coordinate: ((30*25) + (60*35) + (80*45)) / (30+60+80) = 46.25
Y-coordinate: ((20*20) + (50*30) + (70*40)) / (20+50+70) = 32.5

The center of gravity for A, B, and C is at (46.25, 32.5).

Next, we need to calculate the center of gravity for the two distribution centers D and E:

X-coordinate: ((90*60) + (120*70)) / (90+120) = 66.67
Y-coordinate: ((60*50) + (100*60)) / (60+100) = 57.14

The center of gravity for D and E is at (66.67, 57.14).

Now we can calculate the load-distance score for Plant 1 and Plant 2:

Load-Distance score for Plant 1:
- Distance from Plant 1 to A: |46.25-25| + |32.5-20| = 51.25
- Distance from Plant 1 to B: |46.25-35| + |32.5-30| = 16.25
- Distance from Plant 1 to C: |46.25-45| + |32.5-40| = 17.75
- Total score for Plant 1: (30*51.25) + (60*16.25) + (80*17.75) = 4,275

Load-Distance score for Plant 2:
- Distance from Plant 2 to D: |66.67-60| + |57.14-50| = 14.81
- Distance from Plant 2 to E: |66.67-70| + |57.14-60| = 7.58
- Total score for Plant 2: (90*14.81) + (120*7.58) = 2,109.8

The total load-distance score for the two plants is 4,275 + 2,109.8 = 6,384.8. This is more than 300 but less than or equal to 350, so the answer is B.

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