Malhotra Company has four distribution centers located at the location coordinates given as follows. The monthly demand at each center is also given. Management wants to build a new plant that would be located at the center of gravity of the four distribution centers. Which of the following options best represents the coordinates of new plant location? $$\begin{array} { | l | l | l | }
\hline D C & \text { Coordinates } & \text { Demand } \
\hline A & ( 100,150 ) & 50 \
B & ( 250,250 ) & 30 \
C & ( 150,150 ) & 15 \
D & ( 200,300 ) & 100 \
\hline
\end{array}$$
A) x- coordinate is greater than 170 but less than 190; y- coordinate is greater than 230 but less than 250
B) x- coordinate is greater than 150 but less than 170; y- coordinate is greater than 230 but less than 250
C) x- coordinate is greater than 170 but less than 190; y- coordinate is greater than 210 but less than 230
D) x- coordinate is greater than 150 but less than 170; y- coordinate is greater than 210 but less than 230

Question

Malhotra Company has four distribution centers located at the location coordinates given as follows. The monthly demand at each center is also given. Management wants to build a new plant that would be located at the center of gravity of the four distribution centers. Which of the following options best represents the coordinates of new plant location? $$\begin{array} { | l | l | l | } 
\hline D C & \text { Coordinates } & \text { Demand } \
\hline A & ( 100,150 ) & 50 \
B & ( 250,250 ) & 30 \
C & ( 150,150 ) & 15 \
D & ( 200,300 ) & 100 \
\hline
\end{array}$$
A) x- coordinate is greater than 170 but less than 190; y- coordinate is greater than 230 but less than 250
B) x- coordinate is greater than 150 but less than 170; y- coordinate is greater than 230 but less than 250
C) x- coordinate is greater than 170 but less than 190; y- coordinate is greater than 210 but less than 230
D) x- coordinate is greater than 150 but less than 170; y- coordinate is greater than 210 but less than 230

Quizplus · Accepted Answer

The center of gravity is calculated as the weighted average of the coordinates of the distribution centers, where the weights are the demands. The x-coordinate of the center of gravity is (50*100 + 30*250 + 15*150 + 100*200) / (50 + 30 + 15 + 100) = 175. The y-coordinate of the center of gravity is (50*150 + 30*250 + 15*150 + 100*300) / (50 + 30 + 15 + 100) = 237.5. Therefore, the coordinates of the new plant location are (175, 237.5), which is in the range of x-coordinate greater than 170 but less than 190 and y-coordinate greater than 230 but less than 250.

Malhotra Company Has Four Distribution Centers Located at the Location