Problem $3$: $(20$ points$)$

A machine shop has $5$ departments to be assigned to $5$ rooms. The current layout is

$\backslash$table$[[$Room $1,$Room $2,$Room $3,$Room $4,$Room $5],[$Dept$.$ A$,$Dept. B$,$Dept. C$,$Dept. D$,$Dept. E$],[,,,,]]$

The number of material moves or trips between departments are

$\backslash$table$[[$From $\frac{\frac{?}{?}}{?}$ to$,$A$,$B$,C,$D$],[$A$,,10,,40],[$B$,,,30,],[C,,,,30],[$D$,,,,]]$

The cost of one trip between rooms i and $j$ is AED $0\mathrm{.}2$ multiplied by the distance between i and $j.$ a$-$ Determine the "load x Distance" of the current layout