Student enrolment and class scheduling for a private language school business

This paper studies the class scheduling and managerial issues involved for a private language school. A linear programming formulation is used to find the optimal class schedule subject to considerations such as total teacher's salary and classroom capacity. To maximise the profit from enrolment increase, and decide whether to open new sessions or put a cap on enrolment instead of accepting more students, the school needs to ensure any proposed new class brings a positive net income to the business. The marginal profit due to additional enrolment is discussed to determine if new classes will be offered.