it is supply chain, plz show all work thanks

Problem 1. A new coffee shop is to be opened on a college campus. The university administration aims to locate the shop at a location that minimizes the total weighted distance from individual schools including School of Medicine, Business School, College of Arts and Sciences, College of Liberal Arts and College of Engineering based on Euclidian locations. The XY locations for these schools are (0,0),(50,100),(500,500),(250,500), and (500,50) respectively. The student population sizes are 500,1000,800,200, and 300 respectively. Identify the optimal location for the new shop based on the objective of the university administration