A company needs to locate three departments (X, Y, and Z) in the three areas (I, II, and III) of a new facility. They want to minimize interdepartmental transportation costs, which are expected to be $.50 per load meter moved. An analyst has prepared the following flow and distance matrices: $\begin{array}{l}
\text { Distances (meters) } \quad\quad\quad\quad\quad\quad \text { Flows (loads per week }\
\begin{array}{rlll}
\text { From/To } & \text { I } & \text { II } & \text { III } \
\hline \text { I } & - & 10 & 20 \
\text { II } & & - & 10 \
\text { III } & & & -
\end{array}\quad\quad
\begin{array}{rlll}
\text { From/To } & \mathrm{X} & \mathrm{Y} & \mathrm{Z} \
\hline \mathrm{X} & - & 0 & 80 \
\mathrm{Y} & 30 & - & 150 \
\mathrm{Z} & 100 & 130 & -
\end{array}
\end{array}$ What are total weekly costs for an optimum layout?
A) $2,600
B) $3,600
C) $6,200
D) $7,200
E) $8,200

Question

Quizplus · Accepted Answer

The total weekly cost for an optimum layout is $2,600. This is calculated by multiplying the flow between each pair of departments by the distance between their assigned areas and summing the results. For example, the flow between departments X and Y is 30 loads per week, and the distance between areas I and II is 10 meters. Therefore, the cost of transporting loads between departments X and Y is 30 * 10 * $0.50 = $150. The total cost is the sum of all these costs: $150 + $1,300 + $1,150 = $2,600.

A Company Needs to Locate Three Departments (X, Y, and Z)