Table 11.6
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 11.6.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. )

Question

Table 11.6
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 11.6.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. )

Quizplus · Accepted Answer

To find the center of gravity for plants serving A, B, and C, we first need to calculate the total demand for each of these locations:

- Demand at A = 60
- Demand at B = 150
- Demand at C = 90
- Total demand = 60+150+90 = 300

Next, we can calculate the x and y coordinates for the center of gravity using the formula:

x-coordinate = (Demand at A * x-coordinate A) + (Demand at B * x-coordinate B) + (Demand at C * x-coordinate C) / Total Demand
y-coordinate = (Demand at A * y-coordinate A) + (Demand at B * y-coordinate B) + (Demand at C * y-coordinate C) / Total Demand

Substituting the values for x and y coordinates and demands, we get:

x-coordinate = ((60*20)+(150*60)+(90*70))/300 = 57
y-coordinate = ((60*20)+(150*50)+(90*40))/300 = 47

Therefore, the center of gravity for plants serving A, B, and C is at (57, 47).

Similarly, we can calculate the center of gravity for plants serving D and E:

- Demand at D = 120
- Demand at E = 80
- Total demand = 120+80 = 200

x-coordinate = (Demand at D * x-coordinate D) + (Demand at E * x-coordinate E) / Total Demand
y-coordinate = (Demand at D * y-coordinate D) + (Demand at E * y-coordinate E) / Total Demand

Substituting the values, we get:

x-coordinate = ((120*30)+(80*50))/200 = 40
y-coordinate = ((120*70)+(80*20))/200 = 50

Therefore, the center of gravity for plants serving D and E is at (40, 50).

Using Euclidean distance formula, we can calculate the load-distance score for Plant 1 and Plant 2:

- Distance between Plant 1 and A = sqrt((57-20)^2+(47-10)^2) = 49.2
- Distance between Plant 1 and B = sqrt((57-60)^2+(47-50)^2) = 3.6
- Distance between Plant 1 and C = sqrt((57-70)^2+(47-40)^2) = 15.6
- Distance between Plant 2 and D = sqrt((40-30)^2+(50-70)^2) = 20
- Distance between Plant 2 and E = sqrt((40-50)^2+(50-20)^2) = 31.6

Total load-distance score = (60*49.2)+(150*3.6)+(90*15.6)+(120*20)+(80*31.6) = 27024

Therefore, the total load-distance score for the two plants is more than 260 but less than or equal to 280. The best choice would be C.

Table 11.6 Union Fork,Inc.has Five Distribution Centers Located at the Location Coordinates