Table 914
the Department of Philosophy at a University in Oregon

Table 9.14
The department of philosophy at a university in Oregon must allocate six faculty members to their new offices. The following trip matrix indicates the expected number of contacts per day made between professors. Also shown on the right is a sketch of the available office spaces (1 through 6) for the six faculty members. Assume equally sized offices. The distance between office 1 and office 2 (as well as the distance between office 1 and 3) is one unit of distance. Please measure by rectilinear distance.
Trips Between Departments
$$\begin{array} { | c | c | c | c | c | c | c | } \hline & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } \\\hline \mathrm { A } & - - & 0 & 4 & 0 & 0 & 0 \\\mathrm {~B} & & - & 0 & 12 & 0 & 10 \\\mathrm { C } & & & - & 2 & 7 & 0 \\\mathrm { D } & & & & - & 0 & 4 \\\mathrm { E } & & & & & - & 0 \\\mathrm {~F} & & & & & & - \\\hline\end{array}$$
Layout of Available Offices
$$\begin{array} { | c | c | } \hline 1 & 2 \\\hline 3 & 4 \\\hline 5 & 6 \\\hline\end{array}$$
-The trip matrix and the current block plan for a company follow.The two cells in the block plan marked with "ES" are empty space.Assume that material is moved according to rectilinear distances and that the distance between adjacent centers is one unit.It costs $1 to move one unit of material over one unit of distance.
Trips Between Centers
$$\begin{array} { | c | c | c | c | c | } \hline & 1 & 2 & 3 & 4 \\\hline 1 & - & 30 & 30 & 0 \\2 & & - & 60 & 0 \\3 & & & - & 30 \\4 & & & & - \\\hline\end{array}$$
Current Block Plan
$$\begin{array} { | c | c | } \hline 1 & 2 \\\hline 4 & \mathrm { ES } \\\hline 3 & \mathrm { ES } \\\hline\end{array}$$
To reduce materials-handling costs,the following revised block plan is being considered.
$$\begin{array} { | c | c | } \hline 1 & 2 \\\hline 4 & 3 \\\hline \mathrm { ES } & \mathrm { ES } \\\hline\end{array}$$
Compute the "total cost" of each plan (current and revised) ,along with their cost difference.The total cost savings of changing over to the revised block plan is

A) less than or equal to 50.
B) more than 50 but less than or equal to 80.
C) more than 80 but less than or equal to 110.
D) more than 110.