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 meter moved. An analyst has prepared the following flow and distance matrices: $\begin{array}{l}\text { Distances (meters) } \quad\quad\quad\quad\quad\quad \text { Flows (loads per week }\\\begin{array}{rlll}\text { From/To } & \text { I } & \text { II } & \text { III } \\\hline \text { I } & - & 10 & 20 \\\text { II } & & - & 10 \\\text { III } & & & -\end{array}\quad\quad\begin{array}{rlll}\text { From/To } & \mathrm{X} & \mathrm{Y} & \mathrm{Z} \\\hline \mathrm{X} & - & 0 & 80 \\\mathrm{Y} & 30 & - & 150 \\\mathrm{Z} & 100 & 130 & -\end{array}\end{array}$ If the company were to locate departments X, Y, and Z in areas 1, 2, and 3, respectively, what would be the total distance (in meters) loads would be moved each week?

A) 3,100
B) 3,600
C) 6,200
D) 6,700
E) 8,200