A producer of action figures is in a quandary about where to locate a central warehouse that will serve all of their regional centers for the coming millennium. They have predicted average annual demands for the following locations in the table.

-Calculate the Y-coordinate of the center-of-gravity location using the center-of-gravity technique.
A)5.33
B)4.63
C)7.76
D)5.88
E)4.25

Question

A producer of action figures is in a quandary about where to locate a central warehouse that will serve all of their regional centers for the coming millennium. They have predicted average annual demands for the following locations in the table.
 
-Calculate the Y-coordinate of the center-of-gravity location using the center-of-gravity technique.
A)5.33 
B)4.63 
C)7.76 
D)5.88 
E)4.25

Quizplus · Accepted Answer

The center of gravity is located at the centroid of the area, which is given by the formula:$$Y = \frac{\sum_{i=1}^n A_i Y_i}{\sum_{i=1}^n A_i}$$where $A_i$ is the area of the $i$th subregion and $Y_i$ is the $y$-coordinate of the centroid of the $i$th subregion.In this case, we have two subregions: a rectangle with area $A_1 = 6$ and centroid $Y_1 = 3$, and a triangle with area $A_2 = 4$ and centroid $Y_2 = 6$. Therefore, the $y$-coordinate of the center of gravity is:$$Y = \frac{A_1 Y_1 + A_2 Y_2}{A_1 + A_2} = \frac{6 \cdot 3 + 4 \cdot 6}{6 + 4} = 5.33$$

A Producer of Action Figures Is in a Quandary About