What Is the Optimal Location for These Departments in the Floor

question 65

Essay

What is the optimal location for these departments in the floor plan depicted if the transportation cost is $2 per foot and the departments have a daily number of trips between each other as shown?
Daily Number of Trips Between Departments
$$\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } \\\hline \mathrm { A } & \cdots & 20 & 40 & 60 & 80 \\\hline \mathrm { B } & & \cdots & 10 & 30 & 50 \\\hline \text { C } & & & \cdots & 0 & 15 \\\hline \mathrm { D } & & & & \cdots & 5 \\\hline \text { E } & & & & & \cdots \\\hline\end{array}$$ Floor Plan
$$\begin{array} { l | l | l | l | l } \hline \text { Office Space } 1 & \text { Office Space } 2 & \text { Office Space } 3 & \text { Office Space } 4 & \text { Office Space } 5 \\\hline\end{array}$$ Distance Between Offices
$$\begin{array} { | l | c | c | c | c | c | } \hline \text { Office Space } & 1 & 2 & 3 & 4 & 5 \\\hline \hline 1& \cdots & 10 & 20 & 30 & 40 \\\hline \hline2 & & \cdots & 10 & 20 & 30 \\\hline \hline 3& & & \cdots & 10 & 20 \\\hline \hline 4& & & & \cdots & 5 \\\hline 5 & & & & & \cdots \\\hline\end{array}$$

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Definitions:

Standard Deviation

A measure of the dispersion or variation in a set of values, indicating how much the values differ from the mean.

Mean

The arithmetic average of a set of numbers, calculated by summing them and dividing by the number of numbers.

Area

A quantity expressing the two-dimensional size or extent of a shape or surface, typically measured in square units.

Variance

A measure of dispersion in a set of data points, calculated by taking the average of the squared differences from the mean.