A county wants to build one centrally-located processing facility to serve the county's four recycling drop-off locations. The four drop-offs have characteristics as given in the table below. What is the approximate centre of gravity of these four locations? $$\begin{array} { | l | c | c | c | }
\hline \text { Location } & \text { X-coordinate } & \text { Y-coordinate } & \text { Tonnage } \
\hline \text { Drop-off point A } & 1 & 8 & 10 \
\hline \text { Drop-off point B } & 6 & 7 & 35 \
\hline \text { Drop-off point C } & 6 & 2 & 25 \
\hline \text { Drop-off point D } & 4 & 7 & 50 \
\hline
\end{array}$$
A) 4.75, 6.04
B) 17, 24
C) 33.5, 135.4
D) 6, 4.25
E) 570, 725

Question

A county wants to build one centrally-located processing facility to serve the county's four recycling drop-off locations. The four drop-offs have characteristics as given in the table below. What is the approximate centre of gravity of these four locations? $$\begin{array} { | l | c | c | c | } 
\hline \text { Location } & \text { X-coordinate } & \text { Y-coordinate } & \text { Tonnage } \
\hline \text { Drop-off point A } & 1 & 8 & 10 \
\hline \text { Drop-off point B } & 6 & 7 & 35 \
\hline \text { Drop-off point C } & 6 & 2 & 25 \
\hline \text { Drop-off point D } & 4 & 7 & 50 \
\hline
\end{array}$$
A) 4.75, 6.04
B) 17, 24
C) 33.5, 135.4
D) 6, 4.25
E) 570, 725

Quizplus · Accepted Answer

The center of gravity can be calculated using the formula: $$X = \frac{\sum (x_i \times W_i)}{\sum W_i}$$ and $$Y = \frac{\sum (y_i \times W_i)}{\sum W_i}$$, where $x_i$ and $y_i$ are the coordinates and $W_i$ is the weight (tonnage) for each location. Calculating for X and Y gives us the coordinates (4.75, 6.04), which corresponds to choice A.

A County Wants to Build One Centrally-Located Processing Facility to Serve