The　universal　facility　location　problem　generalizes　several　classical　facility　location　problems,　such　as　the　uncapacitated　facility　location　problem　and　the　capacitated　location　problem　(both　hard　and　soft　capacities).　In　the　universal　facility　location　problem,　we　are　given　a　set　of　demand　points　and　a　set　of　facilities.　We　wish　to　assign　the　demands　to　facilities　such　that　the　total　service　aswell　as　facility　cost　is　minimized.　The　service　cost　is　proportional　to　the　distance　that　each　unit　of　the　demand　has　to　travel　to　its　assigned　facility.　The　open　cost　of　facility　i　depends　on　the　amount　z　of　demand　assigned　to　i　and　is　given　by　a　cost　function　fi(z).　In　this　work,　we　extend　the　universal　facility　location　problem　to　include　linear　penalties,　where　we　pay　certain　penalty　cost　whenever　we　refuse　serving　some　demand　points.　As　our　main　contribution,　we　present　a　(7.88+is　an　element　of)-　approximation　local　search　algorithm　for　this　problem.