the indicated deadline.

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

$\backslash$table$[[$From $\frac{\frac{?}{?}}{?}$ To Materials Welding Drills Lathes Grinders Benders,,,,,,$],[$Materials$,0,125,55,0,0,50],[$Welding$,20,0,0,55,0,0],[$Drills$,25,0,0,0,50,0],[$Lathes$,0,25,0,0,15,0],[$Grinders$,50,0,70,0,0,0],[$Benders$,5,0,25,0,0,0]]$

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

$\backslash$table$[[$Room $1,0,20,40,20,40,60],[$Room $2,20,0,20,40,20,40],[$Room $3,40,20,0,60,40,20],[$Room $4,20,40,60,0,20,40],[$Room $5,40,20,40,20,0,20],[$Room $6,60,40,20,40,20,0]]$

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

Which other two rooms should also be placed next to each other, and why?

Based on the information given earlier, please develop a distance table for the following layout. $($Note: You will get confused here! But, the table below displays the room assignments to departments. Table $3$ shows the distances between rooms without taking department assignments into account. You still need the table that shows the distance between departments.$)$

Room $1=$ Benders Room $2=$ Materials Room $3=$ Welding

Room $4=$ Drills Room $5=$ Grinders Room $6=$ Lathes

$4.$ Please calculate the cumulative distance of the layout based on the table developed in $q3$ and the flow matrix given earlier. Please demonstrate the process, specifically show the tables involved and the Excel formula used to calculate the cumulative distance.

$5.$ What are your thoughts on the plan? Please provide your feedback.