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 $ $0\mathrm{.}5$ per load per meter moved. An analyst has prepared the following distances and flow matrices:

Distances $($meters$)$

From$/$To I II III

I $-1020$

II $-30$

III $-$

Flows $($loads per week$)$

From$/$To X Y Z

X $-4290$

Y $40-162$

Z $110148-$

What is the weekly interdepartmental transportation cost using the least costly layout $($Round to the nearest whole number$)?$