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

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?