What Is the Optimal Location for These Departments in the Floor

question 41

Essay

What is the optimal location for these departments in the floor plan depicted if the departments have a daily number of trips between each other as shown? The total number of trips is accounted for in the table, so for example, the 16 trips between A and B are some combination of trips from A to B and from B to A.
Daily Number of Trips Between Departments
$\begin{array}{c|c|c|c|c|c|c|c|c|c} & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} & \mathrm{F} & \mathrm{G} & \mathrm{H} & \mathrm{I} \\\hline \mathrm{A} & \cdots & 16 & 18 & 9 & 3 & 9 & 10 & 3 & 14 \\\hline \text { B } & & \cdots & 4 & 12 & 2 & 10 & 19 & 4 & 16 \\\hline \text { C } & & & \cdots & 18 & 3 & 8 & 8 & 0 & 10 \\\hline \text { D } & & & & \cdots & 3 & 14 & 1 & 5 & 7 \\\hline \text { E } & & & & & \cdots & 1 & 17 & 15 & 12 \\\hline \text { F } & & & & & & \cdots & 19 & 15 & 4 \\\hline \text { G } & & & & & & & \cdots & 8 & 17 \\\hline \text { H } & & & & & & & & \cdots & 14 \\\hline \text { I } & & & & & & & & & \ldots\end{array}$
Floor Plan
$$\begin{array} { | l | l | l | } \hline \text { Office Space } 1 & \text { Office Space } 4 & \text { Office Space } 7 \\\hline \text { Office Space } 2 & \text { Office Space } 5 & \text { Office Space } 8 \\\hline \text { Office Space } 3 & \text { Office Space } 6 & \text { Office Space } 9 \\\hline\end{array}$$ Distance Between Offices
$\begin{array}{|c|c|c|c|c|c|c|c|c|c}\hline \text { Office Space } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline 1 & - & 10 & 20 & 10 & 14 & 22 & 20 & 22 & 28 \\\hline 2 & & \cdots & 10 & 14 & 10 & 14 & 22 & 20 & 22 \\\hline 3 & & & \cdots & 22 & 14 & 10 & 28 & 22 & 20 \\\hline 4 & & & & \cdots & 10 & 20 & 10 & 14 & 22 \\\hline 5 & & & & & - & 10 & 14 & 10 & 14 \\\hline 6 & & & & & & \cdots & 22 & 14 & 10 \\\hline 7 & & & & & & & \cdots & 10 & 20 \\\hline 8 & & & & & & & & \cdots & 10 \\\hline 9 & & & & & & & & & \ldots \\\hline\end{array}$

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Definitions:

Simple Interest Rate

The percentage of the principal amount that is paid as interest for a specified period.

Contract

A contract that is recognized and can be enforced by law, formed between two or more participants.

Simple Interest

Simple Interest is a calculation of interest that does not take into account the effect of compounding. It is typically calculated by multiplying the daily interest rate by the principal amount and the number of days that elapse between payments.

Early Redemption

The act of returning a financial instrument, such as a bond, before its maturity date, often subjecting the holder to a penalty or reduced return.