A lens manufacturer has the capability of making three types of lenses. Type A lenses require 4 minutes of grinding, 2 minutes of polishing, and 4 minutes of coating, and produce a profit of $12. Type B lenses require 2 minutes of grinding, 6 minutes of polishing, and 2 minutes of coating, and produce a profit of $10. Type C lenses require 2 minutes of grinding, 4 minutes of polishing, and 4 minutes of coating, and produce a profit of $8. Each day, 360 labor-hours for grinding, 600 labor hours for polishing, and 480 labor-hours for coating are available. How many of each type of lens should be produced each day to maximize the profit? What will be the profit?