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 calculate the weighted average of the coordinates based on the volume of each source. 
The coordinates and volume of each source are as follows:

Source 1: (30, 40) - 500 lbs
Source 2: (20, 20) - 300 lbs
Source 3: (10, 50) - 200 lbs
Source 4: (40, 10) - 400 lbs

We can calculate the total weight by adding up the individual volumes: 500 + 300 + 200 + 400 = 1400 lbs.

To find the X-coordinate of the centre of gravity, we can use the formula:

Xcg = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)

where:
m = mass (volume)
x = X-coordinate

Using the coordinates and volumes from above, we get:

Xcg = (500*30 + 300*20 + 200*10 + 400*40) / 1400
Xcg = 28.125

To find the Y-coordinate, we use a similar formula:

Ycg = (m1y1 + m2y2 + m3y3 + m4y4) / (m1 + m2 + m3 + m4)

Using the coordinates and volumes from above, we get:

Ycg = (500*40 + 300*20 + 200*50 + 400*10) / 1400
Ycg = 31.25

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

East Texas Seasonings Is Preparing to Build One Processing Centre