A widget manufacturer has the capability of making three types of widgets. Type A widgets require 12 minutes on a lathe, 2 minutes on a grinder, and 2 minutes on a drill press, and produce a profit of $10. Type B widgets require 8 minutes on a lathe, 6 minutes on a grinder, and 2 minutes on a drill press, and produce a profit of $20. Type C widgets require 4 minutes on a lathe, 4 minutes on a grinder, and 8 minutes on a drill press, and produce a profit of $30. Each day, 800 minutes of lathe time, 600 minutes of grinder time, and 300 minutes of drill press time are available. How many of each type of widget should be produced each day to maximize the profit? What is the maximum profit?