Question: Consider the optimization problem faced by University ‘A’ administrator who has the task of maximising revenue from student fees subject to the following constraints:

1. There is a total of 1000 places available at University ‘A’ which must be distributed between domestic students and international students
2. The university receives a fixed grant of $G from the Government to covers its operations and may charge international students whatever it likes. (Sounds familiar!).
3. Let denote the number of domestic students enrolled by University ‘A’. The Government wants 900 of the available places to be allocated to domestic students, and imposes a financial penalty of $5 if deviates from 900.
4. The relationship between the number of international students is given by:
   where denotes the number of international students and F denotes the fee charged to each international student.
5. University ‘A’ must fill all 1000 places. That is,

The University Administrator must choose the values of , , and F to maximise the revenue received by the University

1. Write down the University’s revenue function (net of any penalty imposed by the Government). (4 marks)
2. Write down the constraint function(s) facing the University. (2 marks)
3. Write down the Lagrangean function for this problem. (3 marks)
4. Write down the first-order conditions for a constrained local optimum. (5 marks)
5. Derive the values of , and F which satisfy the first-order conditions. (6 marks)

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document