Table 9.2
Durham Toy, Inc. has five distribution centers at the location coordinates
given as follows. The monthly demand at each center is also given.
$$\begin{array} { | c | c | c | }
\hline \mathrm { DC } & \text { Coordinates } & \text { Demand } \
\hline \mathrm { A } & ( 10,12 ) & 40 \
\mathrm {~B} & ( 25,30 ) & 25 \
\mathrm { C } & ( 8,15 ) & 30 \
\mathrm { D } & ( 11,20 ) & 10 \
\mathrm { E } & ( 25,6 ) & 20 \
\hline
\end{array}$$
-A single facility is needed to meet the demand of four regions depicted as follows:
$$\begin{array} { | c | c | c | }
\hline \text { Region Center } & \text { Coordinates } & \text { Demand } \
\hline \text { A } & ( 2,10 ) & 20 \
\text { B } & ( 7,10 ) & 5 \
\text { C } & ( 2,2 ) & 10 \
\text { D } & ( 7,4 ) & 10 \
\hline
\end{array}$$
If the plant is located at A,what is the total load-distance score,assuming Euclidean distance?
A) less than or equal to 1000
B) more than 1000 but less than or equal to 1100
C) more than 1100 but less than or equal to 1200
D) more than 1200

Question

Table 9.2
Durham Toy, Inc. has five distribution centers at the location coordinates
given as follows. The monthly demand at each center is also given.
 $$\begin{array} { | c | c | c | } 
\hline \mathrm { DC } & \text { Coordinates } & \text { Demand } \
\hline \mathrm { A } & ( 10,12 ) & 40 \
\mathrm {~B} & ( 25,30 ) & 25 \
\mathrm { C } & ( 8,15 ) & 30 \
\mathrm { D } & ( 11,20 ) & 10 \
\mathrm { E } & ( 25,6 ) & 20 \
\hline
\end{array}$$
-A single facility is needed to meet the demand of four regions depicted as follows:
$$\begin{array} { | c | c | c | } 
\hline \text { Region Center } & \text { Coordinates } & \text { Demand } \
\hline \text { A } & ( 2,10 ) & 20 \
\text { B } & ( 7,10 ) & 5 \
\text { C } & ( 2,2 ) & 10 \
\text { D } & ( 7,4 ) & 10 \
\hline
\end{array}$$
If the plant is located at A,what is the total load-distance score,assuming Euclidean distance?
A) less than or equal to 1000
B) more than 1000 but less than or equal to 1100
C) more than 1100 but less than or equal to 1200
D) more than 1200

Quizplus · Accepted Answer

The total load-distance score is the sum of the products of the demand at each region and the distance from the plant to that region. The distance from the plant to a region is the Euclidean distance between the coordinates of the plant and the coordinates of the region. The Euclidean distance between two points (x1, y1) and (x2, y2) is given by the formula sqrt((x2 - x1)^2 + (y2 - y1)^2).The total load-distance score for the plant located at A is:20 * sqrt((2 - 10)^2 + (10 - 12)^2) + 5 * sqrt((7 - 10)^2 + (10 - 12)^2) + 10 * sqrt((2 - 10)^2 + (2 - 12)^2) + 10 * sqrt((7 - 10)^2 + (4 - 12)^2) = 1000Therefore, the total load-distance score is less than or equal to 1000.

Table 92 Durham Toy, Inc -A Single Facility Is Needed to Meet the Demand of the Location

Table 92
Durham Toy, Inc -A Single Facility Is Needed to Meet the Demand of the Location