Roy Creasey Enterprises, a machine shop, is planning to move to a new, larger location. The new building will be $60$ feet long by $40$ feet wide. Creasey envisions the building as having six distinct production areas, roughly equal in size. He feels strongly about safety and intends to have marked pathways throughout the building to facilitate the movement of people and materials. See the following building schematic.

$\backslash$table$[[\backslash$table$[[$Room$],[1]],\backslash$table$[[$Room$],[2]],$Room$],[$Room$,$Room,Room$],[4,5,6]]$

His foreman has completed a month$-$long study of the number of loads of material that have moved from one process to another in the current building. This information is contained in the flow matrix on the left below. Finally, Creasey also developed a matrix to indicate distances between the work areas shown in the building schematic, shown on the right below.

$\backslash$table$[[,,,,,,],[$From$,$Materials,Welding,Drills Lathes Grinders Benders$],[$Materials$,0,125,50,0,0,55],[$Welding$,25,0,0,50,0,0],[$Drills$,20,0,0,0,55,0],[$Lathes$,0,25,0,0,15,0],[$Grinders$,50,0,70,0,0,0],[$Benders$,10,0,15,0,0,0]]$

$\backslash$table$[[,11,2,3,4,5,6],[1,-,20,40,20,40,60],[2,-,-,20,40,20,40],[3,-,-,-,60,40,20],[4,-,-,-,-,20,40],[5,-,-,-,-,-,20],[6,-,-,-,-,-,-]]$

Based on the flows shown in the matrix, it is likely that the processes Material and Welding are in rooms next to each other as they have the highest number of moves between each other.