As to which of the four men’s Majors makes the most profit, the simple, technical answer is The Masters. Each Major is operated by a different body, and Augusta National, a private members club, is the only one of the four that is a business. The other three are not-for-profit organisations.
The Open Championship is run by the R&A; the US Open by the United States Golf Association and the PGA Championship by the PGA of America. These bodies all spend any excess money they accrue from hosting their Majors – in effect the difference between expenditure and revenue – for the good of the game.