A widget manufacturer has the capability of making three types of widgets. Type A widgets require 14 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, 5 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, 720 minutes of lathe time, 460 minutes of grinder time, and 280 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?