If you are asking about exemption from real estate taxes, you are asking a question of state law that varies in every state. Usually, however, a nonprofit school can qualify for local exemption.  Some states require at least a small amount of subsidy for the program, usually coming from contributions, but I am not aware of any state that would weigh a percentage of tuition versus sales in making the determination.

At the federal level, charities do not have to pay tax on income generated from activities related to their exempt purpose, and a culinary arts school could sell meals to the public without taxation if they were produced by the students as part of their training.  The sales would be treated the same as admission tickets from an exempt drama or dance group, payments for providing services in the sheltered workshop, or tickets for the university’s football or basketball games.   The issue is not whether the sale is profitable.  (Division I sports can be hugely profitable.)  The issue is whether the sale is related to the exempt purpose of the organization. This type of sale would not be deemed unrelated business taxable income and would not be subject to unrelated business income tax (UBIT). (See Ready Reference Page:  “Nonprofit Often Worry About UBIT”)