Using the following information about material volume shipped from a plant to four retail outlets, which of the following is a TRUE statement about the center of gravity for the best location of the plant? $\begin{array}{rrr}\text { Reta1 Outlet }&\text { Location Coordinates } \mathrm{X}, \mathrm{Y}&\text { Material Movement }\
1 & 18,6 & 1,500 \
2 & 12,15 & 2,100 \
3 & 7,10 & 1,900 \
4 & 7,20 & 1,200
\end{array}$
A) The x-axis and the y-axis are less than 10.0.
B) The x-axis is less than 10.0, and the y-axis is more than 10.0.
C) The x-axis is more than 10.0, and the y-axis is less than 10.0.
D) The x-axis and the y-axis are more than 10.0.

Question

Quizplus · Accepted Answer

The center of gravity (CoG) can be calculated using the formula for the weighted average of the locations, taking into account the material movement (weight). For the x-coordinate: $\frac{(18 \times 1500) + (12 \times 2100) + (7 \times 1900) + (7 \times 1200)}{1500 + 2100 + 1900 + 1200} = \frac{27,000 + 25,200 + 13,300 + 8,400}{6700} = \frac{73,900}{6700} \approx 11.03$. For the y-coordinate: $\frac{(6 \times 1500) + (15 \times 2100) + (10 \times 1900) + (20 \times 1200)}{1500 + 2100 + 1900 + 1200} = \frac{9,000 + 31,500 + 19,000 + 24,000}{6700} = \frac{83,500}{6700} \approx 12.46$. Both x and y coordinates of the center of gravity are more than 10.0.

Using the Following Information About Material Volume Shipped from a Plant