Using the following information about material volume shipped from a factory to four retail outlets, find the best location for the factory using the center-of-gravity method. $\begin{array}{|c|c|c|}\hline \text { RETAIL } & \text { LOCATION COORDINATES } & \text { MATERIAL } \
\text { OUTLET } & \underline{\mathrm{X} Y \mathrm{Y}} & \text { MOVEMENT } \
\hline 1 & 18,6 & 1,500 \
\hline 2 & 12,15 & 2,100 \
\hline 3 & 7,10 & 1,900 \
\hline 4 & 7,20 & 1,200 \
\hline
\end{array}$ Which one of the following statements is TRUE for this set of center-of-gravity data?
A) Cx is less than 10.00 and Cy is more than 10.00.
B) Cx is more than 10.00 and Cy is less than 10.00.
C) Cx is less than 10.00 and Cy is less than 10.00.
D) Cx is more than 10.00 and Cy is more than 10.00.

Question

Quizplus · Accepted Answer

To find the center of gravity (Cx, Cy) for the factory location, we use the formula: $$Cx = \frac{\sum (X_i \times Q_i)}{\sum Q_i}$$ $$Cy = \frac{\sum (Y_i \times Q_i)}{\sum Q_i}$$ where $X_i$ and $Y_i$ are the coordinates of each retail outlet, and $Q_i$ is the material movement to that outlet. Calculating Cx: $$Cx = \frac{(18 \times 1500) + (12 \times 2100) + (7 \times 1900) + (7 \times 1200)}{1500 + 2100 + 1900 + 1200}$$ $$Cx = \frac{27000 + 25200 + 13300 + 8400}{6700}$$ $$Cx = \frac{73900}{6700} \approx 11.03$$ Calculating Cy: $$Cy = \frac{(6 \times 1500) + (15 \times 2100) + (10 \times 1900) + (20 \times 1200)}{1500 + 2100 + 1900 + 1200}$$ $$Cy = \frac{9000 + 31500 + 19000 + 24000}{6700}$$ $$Cy = \frac{83500}{6700} \approx 12.46$$ Therefore, Cx is more than 10.00 and Cy is more than 10.00.

Using the Following Information About Material Volume Shipped from a Factory