Problem $4.$

Richard Garber is the head designer for Matthews and Novak Design Company. Garber has been called in to design the layout for a newly constructed office building. From statistical samplings over the past three months, Garber developed the following closeness matrix for daily trips between the department's offices.

CLOSENESS MATRIX

$\backslash$table$[[,$Trips Between Departments$],[$Department$,$A$,$B$,$C$,$D$,$E$,$F$],[$A$,-,25,90,,,185],[$B$,,-,,,105,],[$C$,,,-,,125,125],[$D$,,,,-,25,],[$E$,,,,,,105],[$F$,,,,,,-]]$

Alternative Block Plan:

$\backslash$table$[[$C$,$F$,$A$],[$B$,$E$,$D$]]$

a$.$ If other factors are equal, which two offices should be located closest together?

b$.$ Figure $3\mathrm{.}15$ shows an alternative layout for the department. What is the total weighted$-$distance score for this plan based on rectilinear distance and assuming that offices A and B are three units of distance apart?