A job shop has four departments milling $($M$),$ drilling $($D$),$ sawing $($S$),$ and assembly $($A$)$assigned to four work areas. The operations manager, Sergio Barba, has gathered the following data for the movement of material.

The number of workpieces moved yearly between work areas are:

$\backslash$table$[[,$M$,$D$,$S$,$A$],[$M$,0,100,20,20],[$D$,50,0,30,0],[$S$,0,170,0,80],[$A$,20,20,30,0]]$

a$.$ Which department should be located next to the sawing department based on flows?

b$.$ Which department has the highest flow between the assembly department?

c$.$ The distances between departments is

$\backslash$table$[[,$M$,$D$,$S$,$A$],[$M$,,20,40,60],[$D$,,,20,40],[$S$,,,,20],[$A$,,,,]]$

Calculate the cost of the layout if it cost $$1\mathrm{.}50$ to move a part.