Answer to Question #306370 in Linear Algebra for shambhav

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?

 

X-coordinate

Y-coordinate

Volume

Athens, Texas

30

30

150

Beaumont, Texas

20

10

350

Carthage, Texas

10

70

100

Denton, Texas

50

50

200

 

Answer 1

$\sum\>x_iV_i=(30×150)+(20×350)+(10×100)+(50×200)$

$=22500$

$\sum\>y_1V_1=(30×150)+(10×350)+(70×100)+(50×200)$

$=25000$

$\sum\>V=150+350+100+200$

$=800$

$x_c=\frac{22500}{800}=28.125$

$y_c=\frac{25000}{800}=31.25$