A manufacturing concern has five departments $($labeled A through E$)$ located in a rectangular building as shown below:

$\backslash$table$[[$Flow$-$between Matrix$],[,$A$,$B$,$C$,$D$,$E$],[$A$,-,0,5,0,5],[$B$,,-,6,2,0],[$C$,,,-,3,0],[$D$,,,,-,7],[$E$,,,,,-]]$

$\backslash$table$[[$Unit cost $($$$/$Unit Dist.$)],[,$A$,$B$,$C$,$D$,$E$],[$A$,-,0,1,0,1],[$B$,,-,1,4,0],[$C$,,,-,3,0],[$D$,,,,-,1],[$E$,,,,,-]]$

$\backslash$table$[[$Distance Matrix$],[,$A$,$B$,$C$,$D$,$E$],[$A$,-,6,19,18,11],[$B$,,-,12,22,15],[$C$,,,-,10,8],[$D$,,,,-,7],[$E$,,,,,-]]$

a$)(4$ points$)$ Using the CRAFT two$-$way exchange procedure, indicate all the department pairs CRAFT would consider exchanging in the above layout.

b$)(5$ points$)$ Compute the estimated cost of exchanging departments A and E $.($The Distance Matrix gives the approximate distance between departments for the current given layout, and you can directly use it$.)$