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: Rectilinear

Objective: Minimizing cost

Coordinates of the existing machines $(5,9),(4,4),(10,12),(11,20),(7,15)$

Total weight of material to be moved between the new machine and the existing ones: $15000,21500,29000,23000$ and $7000$ pounds per week, respectively.

$($B$)$ Calculate cost in distance$-$weight units.