Franky has been given the job of developing a process layout for an Amazon warehouse, with the goal of minimizing the total transportation of material. Assign departments $1$ through $5$ to locations A through $E($which are separated by the distances shown in the left table$)$ in such a way that transportation cost $($$$2\mathrm{.}50/$meter$)$ is minimized. Franky has been told to assign departments with the greatest interdepartmental workflow first to locations that are closest to each other.

DISTANCE BETWEEN LOCATIONS $($meters$)$

$\backslash$table$[[$From $/$ To$,$A$,$B$,$C$,$D$,$E$],[$A$,-,80,130,70,200],[$B$,,-,30,50,90],[$C$,,,-,60,40],[$D$,,,,-,110],[$E$,,,,,-]]$

TRIPS BETWEEN DEPARTMENTS $($per day, bidirectional$)$

$\backslash$table$[[$From $|$ To$,1,2,3,4,5],[1,-,10,20,76,68],[2,,-,40,92,42],[3,,,-,57,80],[4,,,,-,24],[5,,,,,-]]$

Layout of locations: