$($A$)$ Use the appropriate location procedure to determine the optimal coordinates of a new machine based on the following assumptions. $($Please show the details of your work: Not just the final answer$).$Traffic pattern: RectilinearObjective: Minimizing costCoordinates of the existing machines $(5,2),(4,8),(10\mathrm{.}12),(3,20),(7\mathrm{.}7)$Total weight of material to be moved between the new machine and the existing ones: $11000,27500,22000,3000$ and $17000$ pounds per week, respectively.$($B$)$ Calculate cost in distance$-$weight units.Note: No points will be awarded if the wrong location model is used.