East Texas Seasonings is preparing to build one processing centre 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 centre of gravity?
A)X = 28.125;Y = 31.25
B)X = 22000;Y = 24000
C)X = 27.5;Y = 40
D)centre of gravity = 24000
E)centre of gravity = 28

Question

East Texas Seasonings is preparing to build one processing centre 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 centre of gravity? 
A)X = 28.125;Y = 31.25 
B)X = 22000;Y = 24000 
C)X = 27.5;Y = 40 
D)centre of gravity = 24000 
E)centre of gravity = 28

Quizplus · Accepted Answer

To find the centre of gravity, we need to use the formula:

Xcg = (ΣXiVi) / ΣVi
Ycg = (ΣYiVi) / ΣVi

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

Plugging in the values, we get:

Xcg = [(22 * 10) + (30 * 15) + (25 * 18) + (35 * 12)] / (10 + 15 + 18 + 12) = 28.125
Ycg = [(35 * 10) + (20 * 15) + (25 * 18) + (20 * 12)] / (10 + 15 + 18 + 12) = 31.25

Therefore, the centre of gravity is at coordinates (28.125, 31.25), which is choice A.

East Texas Seasonings Is Preparing to Build One Processing Centre