Question

Question 3 (20 marks) Consider the optimization problem faced by a Monash University administrator who has the task of maximizing revenue from student fees subject to the following constraints: 1. There is a total of 1000 places available at Monash which must be distributed between domestic students and international students 2、 The University receives a fixed grant of SG from the Government to cover its operations, and may charge international students whatever it likes. (Sound familiar!) 3. Letxdenote the number of domestic students enrolled by Monash. The Government wants 900 of the available places to be allocated to domestic students, and imposes a financial penalty of S5(900-xi)2 if xideviates from 900 4. The relationship between the number of international students who wish to attend the University and the fee charged to international students is given by 2250- where x2 denotes the number of international students and F denotes the fee charged to each international student. 5. Monash must fill all 1000 places. That is, +x21000 The University Administrator must choose the values of xi, x2 and F to maximize the revenue received by the University (a) Write down the University's revenue function (net of any penalty imposed by the Government) 4 marks) b) Write down the constraint function(s) facing the University (2 marks) (c) Write down the Lagrangean function for this problem. (3 marks) (d) Write down the first-order conditions for a constrained local optimum. (5 marks) (e) Derive the values of x,2 and F which satisfy the first-order conditions. 6 marks)

Answer 1

ion Given thel 거『na.et domebhc sんdu.h Revenue lunchon pot +寵venue due foin 코。 Cons taint 旬 function-X, 1 L a gsangea on tot a constsained letal opámum Subs hack O&② 20K (150-120) = 2-O K 136 F = 。2600