Good Day, Please help with developing a nonlinear programming model for the case study

A University of Technology has increased its tuition fees for local and foreign students in each of the past five years to offset cuts in its subsidy from the government. The university administration was of the view that the number of applications received from students was independent of tuition fees. However, a reduction in the number of applications and enrolments over the past two years have proved otherwise. Admissions officials have developed the following relationships between the number of applicants who accept admission and enrol at the university and tuition fees per semester:

x₁ = 20 000 12c₁ (local students)

x₂ = 30 000 6c₂ (foreign students)

where x₁ = number of local students

x₂ = number of foreign students

c₁ = tuition fees of local students

c₂ = tuition fees of foreign students

The university wants to develop a model that will indicate the tuition fees of local and foreign students, as well as the number of students that could be expected to enrol in the first year of study. The university does not have enough classroom space for more than 1 500 first year students, and it needs at least 800 first year students to meet the objectives of its class size.

Historical data shows that approximately 50% of all local first year students will require university residences, 75% of all foreign students will require university residences, and the maximum number of rooms available at the residences for first year students is 800 rooms.

The university also wants to maintain its high academic standards in its admissions policy. It knows from historical data that the average Aptitude Test Scores (ATS) for a local student is 76 and the average ATS score for a foreign student is 95. The university require students entering the first year of study to have an average ATS score of at least 80.

The University of Technology is a government-subsidised academic institution. The government wants to ensure that the university does not enrol only foreign students because they pay more tuition fees and they have better ATS scores than local students. Hence, the government has instituted a policy that no more than 55% of the students entering the first year of study can be foreign students.

Develop a nonlinear programming model for University of Technology indicating the following:

the tuition fees that the university should charge each student,

the total tuition fees that the university can expect to collect from students, and

the number of local and foreign students the university can expect with these tuition fees.