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:

Net Income

The total revenue of a business minus total expenses, indicating the profit earned over a specific period.

Depreciation Method

A systematic approach used to allocate the cost of a tangible asset over its useful life.

Double Declining-Balance

An accelerated method of depreciation which doubles the normal depreciation rate, reducing the value of an asset more quickly in its early years.

Straight-Line Method

A technique for calculating an asset's depreciation by uniformly distributing its cost throughout its anticipated lifespan.