East Texas Seasonings is preparing to build one processing center to serve its four sources of seasonings.The four source locations are at coordinates shown below.Also,the volume from each source is provided.What is the center of gravity?
A)X = 28.125;Y = 31.25
B)X = 22000;Y = 24000
C)X = 27.5;Y = 40
D)center of gravity = 28
E)X = 25;Y = 40

Question

East Texas Seasonings is preparing to build one processing center to serve its four sources of seasonings.The four source locations are at coordinates shown below.Also,the volume from each source is provided.What is the center of gravity? 
A)X = 28.125;Y = 31.25 
B)X = 22000;Y = 24000 
C)X = 27.5;Y = 40 
D)center of gravity = 28 
E)X = 25;Y = 40

Quizplus · Accepted Answer

To find the center of gravity, we need to calculate the weighted average of the coordinates of each source location, with the volume as the weight. Using the formula:

Xcg = (∑(XiVi)) / ∑Vi 
Ycg = (∑(YiVi)) / ∑Vi

Where Xi and Yi are the x and y coordinates of each source location, Vi is the volume from that source.

Plugging in the values:

Xcg = ((25*5000) + (30*8000) + (35*6000) + (28*4000)) / (5000 + 8000 + 6000 + 4000) = 28.125 
Ycg = ((30*5000) + (35*8000) + (25*6000) + (31*4000)) / (5000 + 8000 + 6000 + 4000) = 31.25

Therefore, the center of gravity is at coordinates (28.125, 31.25), which corresponds to answer choice A.

East Texas Seasonings Is Preparing to Build One Processing Center