An American university has enough places for 9000 students. Government restrictions mean that at least 75% of the places must be given to US students but the remainder may be given to non-US citizens. There are 5000 residential places available on campus. All overseas students and at least one-quarter of the US students must be given places on campus. The university gets $12 000 in tuition fees for each US student and $15 000 for each overseas student. It wants to maximise the fees received. Using the letter x for the number of places given to US students and y for the number of places for overseas students,
(a) write down an expression for the objective function and state whether it is to be maximised or minimised;
(b) write down the five constraints that define the feasible region and explain your reasoning carefully;
(c) identify which aspect of the original problem has been overlooked in parts (a) and (b).
