Solve Problem $12\mathrm{.}7($a$)$ described below.

The production area of the XYZ Machine Company is a processtype layout. The present layout is as follows:

A C

D E

B F

In the layout above, $A,B,C,D,E,$ and $F$ are the six processing areas. For safety reasons, it is undesirable to place areas A and F adjacent to each other. A study of the manufacturing activities of the XYZ Machine Company indicated that four major products accounted for $85\%$ of the total manufacturing activity in the above production area last year. The production sequence of these products and the number of units produced per year can be found in the following table.

$\backslash$table$[[$Product$,$Production Sequence,Number c$],[$Produced$,$Number of Units,$],[$Week$,$per Trip,$],[1,$B$-$E$-$F$,],[8000,50,],[\backslash$table$[[2],[25]],$A$-$D$-$E$-$F$,500],[\backslash$table$[[3],[50]],$C$-$B$-$E$-$A$,5000],[4,\backslash$table$[[$A$-$C$-$B$-$E$-$F$],[100]],15,000]]$

Standard $36$ x $36-$inch unitized pallets and a conventional narrow aisle for a lift truck are the material$-$handling equipment involved in the production of the four products. The average number of units carried per trip by the lift truck are also indicated in the above table $($assume one unit of area for each department$).$

$($a$)(20$ points$)$ Develop an activity rel$-$chart according to the codes:

A is above $25000.$

E: $10000-25000$

I: $5000-9999$

O: $100-4999$

$U$ is below $100.$

$($b$)(10$ points$)$ Convert the rel$-$chart into a value chart.

$($c$)(20$ points$)$ Assume the distance between two departments