A manufacturer of automotive air conditioners currently operates three assembly plants at the locations with coordinates A (150, 75), B (100,300) and C (275, 380), and source their compressors externally. The company is considering producing its compressors in-house, and would like determine the most central location for a production plant, considering the volumes shipped. The Demand for compressors at each of the three assembly plants are A (6,000), B (8,200) and C (7,000). Determine the most suitable location for their new compressor manufacturing plant, considering the volume of compressors to be shipped from the proposed compressor manufacturing plant to the three air-conditioner assembly plants.