A Company Needs to Locate Three Departments (X, Y, and Z)

A company needs to locate three departments (X, Y, and Z) in the three areas (I, II, and III) of a new facility. They want to minimize interdepartmental transportation costs, which are expected to be $.50 per load per meter moved. An analyst has prepared the following distances and flow matrices: $\begin{array}{l}\text { Distances (meters) } \quad\quad\quad\quad\quad\quad \text { Flows (loads per week }\\\begin{array}{rlll}\text { From/To } & \text { I } & \text { II } & \text { III } \\\hline \text { I } & - & 10 & 20 \\\text { II } & & - & 10 \\\text { III } & & & -\end{array}\quad\quad\begin{array}{rlll}\text { From/To } & \mathrm{X} & \mathrm{Y} & \mathrm{Z} \\\hline \mathrm{X} & - & 60 & 90 \\\mathrm{Y} & 40 & - & 160 \\\mathrm{Z} & 110 & 140 & -\end{array}\end{array}$ What is the distance (in meters) from area III to area I in this new facility?

A) 0
B) 10
C) 20
D) 30
E) 40