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

Table $1.$ Building Schematic

Room $1$ Room $2$ Room $3$

Room $4$ Room $5$ Room $6$

The owner$$s 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 below.

Table $2.$ Material Flows

From$\backslash$To Materials Welding Drills Lathes Grinders Benders

Materials $0125550050$

Welding $20005500$

Drills $25000500$

Lathes $02500150$

Grinders $50070000$

Benders $5025000$

Finally, the owner also developed a matrix to indicate distances between the work areas shown in the building schematic, shown on the right below. Please note that this is the distance between rooms, not the actual department.

Table $3.$ Room Distance Table

Distance $($Feet$)$ Room $1$ Room $2$ Room $3$ Room $4$ Room $5$ Room $6$

Room $1-2040204060$

Room $220-20402040$

Room $34020-604020$

Room $4204060-2040$

Room $540204020-20$

Room $66040204020-$

$1.$ Based on the material flows shown in the table $2,$ which one process should be in rooms next to the Welding area and why?