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:

M D S A

M $01002020$

D $500300$

S $0170080$

A $2020300$

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

M D S A

M $204060$

D $2040$

S $20$

A

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