There Are Three Work Centers (A, B, and C) Behind

question 154

Essay

There are three work centers (A, B, and C) behind the financial aid counter at a nearby university. They can each fit into any of three office spaces (1, 2, and 3) off the corridor behind the desk. There is no student contact in these areas, only workers. The distance 1-2 is 20 feet, 2-3 is 30 feet, and 1-3 is 50 feet. The matrix of work (trips per day) at the three centers is in the following table. Remember that each trip must be a round-trip (from 1 to 2 and back, for example).
$$\begin{array} { | c | c | c | c | } \hline & \mathrm { A } & \mathrm { B } & \mathrm { C } \\\hline \mathrm { A } & - - & 20 & 0 \\\hline \mathrm { B } & 45 & - - & 25 \\\hline \mathrm { C } & 60 & 0 & - - \\\hline\end{array}$$
a. How many possible assignments are there?
List them.
b. Calculate the total distance traveled in each of these assignments.
c. Which assignment minimizes distance traveled?

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Definitions:

Hypertension

A chronic medical condition where blood pressure in the arteries is persistently elevated, requiring management to prevent further health complications.

Blood Pressure

The force exerted by circulating blood on the walls of the body's arteries, a critical parameter in assessing cardiovascular health.

Secondary Prevention

Efforts and interventions aimed at early detection and prompt treatment of disease or injury to prevent more severe problems developing.

Congestive Heart Failure

A chronic condition in which the heart is unable to pump blood effectively enough to meet the body's needs, leading to symptoms such as shortness of breath and swelling.