Kim needs to decide which product distribution center to use to supply her four nail salons. The four locations are at coordinates shown in the following table. The volume of products required from by each store is also provided. What is the center of gravity of the distribution center relative to the salons? $$\begin{array} { | l | c | c | c | }
\hline \text { Location } & \text { X-coordinate } & \text { Y-coordinate } & \text { Volume } \
\hline \text { Uptown } & 30 & 70 & 200 \
\hline \text { Midtown } & 40 & 50 & 350 \
\hline \text { Lower East Side } & 50 & 30 & 150 \
\hline \text { Lower West Side } & 10 & 20 & 100 \
\hline
\end{array}$$
A) X = 35.625; Y = 47.50
B) X = 28.50; Y = 38.00
C) X = 28,500; Y = 38,000
D) X = 47.50; Y = 35.625

Question

Kim needs to decide which product distribution center to use to supply her four nail salons. The four locations are at coordinates shown in the following table. The volume of products required from by each store is also provided. What is the center of gravity of the distribution center relative to the salons? $$\begin{array} { | l | c | c | c | } 
\hline \text { Location }  & \text { X-coordinate } & \text { Y-coordinate } & \text { Volume } \
\hline \text { Uptown } & 30 & 70 & 200 \
\hline \text { Midtown } & 40 & 50 & 350 \
\hline \text { Lower East Side } & 50 & 30 & 150 \
\hline \text { Lower West Side } & 10 & 20 & 100 \
\hline
\end{array}$$
A) X = 35.625; Y = 47.50
B) X = 28.50; Y = 38.00
C) X = 28,500; Y = 38,000
D) X = 47.50; Y = 35.625

Quizplus · Accepted Answer

The center of gravity (CoG) is calculated using the formula: $$X_{CoG} = \frac{\sum (X_i \times V_i)}{\sum V_i}$$ and $$Y_{CoG} = \frac{\sum (Y_i \times V_i)}{\sum V_i}$$, where $X_i$ and $Y_i$ are the coordinates and $V_i$ is the volume for each location. Calculating for X: $$X_{CoG} = \frac{(30 \times 200) + (40 \times 350) + (50 \times 150) + (10 \times 100)}{200 + 350 + 150 + 100} = 35.625$$ and for Y: $$Y_{CoG} = \frac{(70 \times 200) + (50 \times 350) + (30 \times 150) + (20 \times 100)}{200 + 350 + 150 + 100} = 47.5$$. Therefore, the center of gravity is at X = 35.625, Y = 47.5.

Kim Needs to Decide Which Product Distribution Center to Use