The Flow and Distance Data in the Table Below Were

question 84

Essay

The flow and distance data in the table below were input into a layout software program, and solved by "pairwise comparison." That solution called for assignments A-4, B-1, C-3, and D-2, with a total movement of 2430. Verify that result. Is that solution optimal? Can you offer an improved solution? What is the total movement of your alternate solution?
$$\begin{array} { | c | c | c | c | c | c | } \hline \text { Flow Table } & \text { A } & \text { B } & \text { C } & \text { D } & \begin{array} { c } \text { Fixed } \\\text { room }\end{array} \\\hline \text { A } & 0 & 5 & 8 & 3 & \\\hline \text { B } & 0 & 0 & 7 & 6 & \\\hline \text { C } & 0 & 2 & 0 & 9 & \\\hline \text { D } & 5 & 12 & 4 & 0 & \\\hline & & & & & \\\hline \text { Distance Table } & \text { Room } 1 & \text { Room } 2 & \text { Room } 3 & \text { Room } 4 & \\\hline \text { Room } 1 & 0 & 30 & 60 & 80 & \\\hline \text { Room } 2 & 30 & 0 & 30 & 50 & \\\hline \text { Room } 3 & 60 & 30 & 0 & 20 & \\\hline \text { Room } 4 & 80 & 50 & 20 & 0 & \\\hline\end{array}$$

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Definitions:

Shares Sold

The quantity of individual stocks that have been purchased by investors and are on the market.

Convertible Preferred Stock

A type of preferred stock that holders can convert into a specified number of common stock shares, usually at any time after a predetermined date.

Common Stock

Shares of ownership in a corporation, giving holders voting rights and a portion of the profits through dividends.

Dividend

A portion of a company's earnings distributed to its shareholders, typically paid regularly (e.g., quarterly).