A small manufacturing facility is being planned that will feed parts to three heavy manufacturing facilities. The locations of the current plants with their coordinates and volume requirements are given in the following table:

PLANT LOCATION COORDINATES $($x$,$ y$)$ VOLUME $($PARTS PER YEAR$)$

Peoria $304,2934,100$

Decatur $377,4726,050$

Joliet $469,1713,100$