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 $$\mathrm{.}50$ 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 $-10$

III $-$

Flows $($loads per week$)$

From$/$To X Y Z

X $-6090$

Y $40-160$

Z $110140-$

What is the distance $($in meters$)$ from area III to area I in this new facility?

Multiple Choice

$10$

$20$

$0$

$30$

$40$