Several practical instances of network design and location theory problems require the network to satisfy multiple constraints. In this paper, we address graph-theoretic problems that aim to simultaneously address a network design task and a location-theoretic constraint. The Budget Constrained Connected Median Problem is the following: We are given an undirected graph 							
						
							
					 															
					Goran Konjevod, Sven Oliver Krumke, Madhav V. Mara