The complicated mission to save 33 men from the collapsed San Jose mine near Copiapo, Chile, which ended successfully Wednesday night, will cost an estimated $10 million to $20 million, according to Chilean President Sebastian Pinera.

Thirty-three men have been trapped in a gold and copper mine in Copiapo, Chile, since it collapsed on Aug. 5. Starting late Tuesday, a pod painted in the colors of the Chilean flag will begin lifting them one-by-one to the…