A private school is run by a private, non-government group. For example, some schools are run by religious organizations or art-focused organizations. Private schools are usually funded by charging tuition, which is a set fee people pay for a service. Many private schools have additional sources of funding such as donations (gifts of money).

Private schools are available at all educational levels, from preschools up through college. Private colleges tend to have higher tuition costs than public universities.

Acompany manufactures x units of product a and y units of product b, on two machines, i and ii. it has been determined that the company will realize a profit of $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 min available on machine ii in each work shift. how many units of a product should be produced in each shift to maximize the company's profit p?