Problem $1(20$ points$)$

Six operations $($A to F$)$ have to be assigned to six departments $(1$ to $6),$ which are arranged according to the

following figure. The numbers on the lines connecting the departments are the walking distances in

meters between the departments.

The following table shows the load between each two operations.

a$-$ Determine the "load x Distance" of the current layout: A$-3,$ B$-1,$ C$-6,$ D$-2,$ E$-4,$ and F$-5.$