A factory manufactures two types of ice skates - racing skates and figure skates. Racing skates require 8 hours of fabrication and 2 hours of finishing while figure skates require 4 hours of fabrication and 2 hours of finishing. The factory's fabrication department has 224 hours available per day and the finishing department has 72 hours available. The problem is to determine the number of each type of skate to manufacture daily to maximize profit, where racing skates yield $15 profit each and figure skates yield $12 profit each.