Problem $3.$ PDM Distributing initially started as a wholesale distributor operating out of Minneapolis. As their reputation for hiqh quality products and logistics services spread, their business expanded throughout the entire United States with a total of $14$ operating locations. The Minneapolis facility has continued to serve as their main distribution center supporting the operating locations.

Due to their expansion into online retailing, PDM Distributing has decided to open two new operating locations in Salt Lake City, UT and Dallas Texas bringing the total number of operating locations to $16.$ Management believes the addition of these two new operating locations will require the company to reposition its central distribution center from Minneapolis to another location. Minneapolis will remain as an operating location but will no longer serve as the central distribution center. Your task is to determine the optimal location for a new central distribution center to support the ten operating locations. The CEO wants to obtain the optimal location coordinates and total cost for the optimal location.