The Times-Picayune is searching for an ideal spotting station for the morning paper. Neighborhoods, their location on an XY grid of the city, and morning volume are shown in the table. What is the location that will minimize the transportation costs for the newspaper? $$\begin{array} { | l | c | c | c | }
\hline { \text { Customer } } & \text { Annual Volume } & \text { X-Coordinate } & \text { Y-Coordinate } \
\hline \text { Florida } & 250 & 3 & 7 \
\hline \text { Desire } & 125 & 7 & 5 \
\hline \text { Lafitte } & 178 & 1 & 3 \
\hline \text { Iberville } & 264 & 2 & 5 \
\hline \text { Guste } & 137 & 1 & 6 \
\hline \text { CJ Peete } & 55 & 1 & 4 \
\hline
\end{array}$$
A)Near (3.1,4.6)
B)Near (4.3,5.8)
C)Near (2.5,5.2)
D)Near (6.4,2.5)

Question

The Times-Picayune is searching for an ideal spotting station for the morning paper. Neighborhoods, their location on an XY grid of the city, and morning volume are shown in the table. What is the location that will minimize the transportation costs for the newspaper? $$\begin{array} { | l | c | c | c | } 
\hline  { \text { Customer } } & \text { Annual Volume } & \text { X-Coordinate } & \text { Y-Coordinate } \
\hline \text { Florida } & 250 & 3 & 7 \
\hline \text { Desire } & 125 & 7 & 5 \
\hline \text { Lafitte } & 178 & 1 & 3 \
\hline \text { Iberville } & 264 & 2 & 5 \
\hline \text { Guste } & 137 & 1 & 6 \
\hline \text { CJ Peete } & 55 & 1 & 4 \
\hline
\end{array}$$
A)Near (3.1,4.6)
B)Near (4.3,5.8)
C)Near (2.5,5.2)
D)Near (6.4,2.5)

Quizplus · Accepted Answer

The ideal location minimizes transportation costs, which can be approximated by finding the weighted average (or centroid) of the locations based on their volumes. Calculating the weighted average of the X and Y coordinates using the formula $\frac{\sum (volume \times coordinate)}{\sum volume}$ for both X and Y coordinates gives a point near (2.5, 5.2), which corresponds to option C.

The Times-Picayune Is Searching for an Ideal Spotting Station for the Morning