Problem $2$

A job shop has four work centers: A$,$ B$,$ C$,$ and D that are currently located in an L$-$shaped facility as in locations $1,2,3,$ and $4$ as shown:

$A$ in $1B$ in $2C$ in $3$

$D$ in $4$

The distance in meters between each pair of locations are as follows:

$\backslash$table$[[,1,2,3,4],[1,,70,160,240],[2,-,-,70,85],[3,-,$E$,-,40],[4,,,,]]$

The loads moved between each pair of work centers per week are as follows:

$\backslash$table$[[,A,$B$,\frac{?}{\text{b}\text{a}\text{r}}(C),$D$],[A,,15,30,60],[$B$,,,15,10],[d,,,,20],[D,,,-,]]$

Material handling cost is $$2$ per load per meter.

a$.$ What is the total material handling cost per week for the current layout?

a$.$ Propose a revised $($best$)$ layout by switching the locations of some centers. What would be the total materials handling cost for this revised layout?