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?

The department that should be located next to the sawing department is drilling. This is because the sawing department has the highest number moved to the drilling department which is $170$ pieces a year.

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

The department that has the highest flow number between the assembly department is sawing department. The number is $30$ pieces per year.

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.