Q3. Ghulam Ishaq Khan University has increased its tuition for in-province and out-of-province students in each of the past 8 years to offset cuts in its budget allocation from the provincial legislature. The university administration always thought that the number of applications received was independent of tuition; however, drops in applications and enrollments the past 3 years have proved this theory to be wrong. University admissions officials have developed the following relationships between the number of applicants who accept admission and enter Ghulam Ishaq Khan (xi) and the cost of tuition per semester (t:) : X1 = 27,000 12t1 (in-province) X2 = 43,000 - 6t2 (out-of-province) The university would like to develop a planning model that will indicate the in-province and out-of-province tuitions, as well as the number of students that could be expected to enroll in the freshman class. The university does not have enough classroom space for more than 1,650 freshmen, and it needs at least 830 freshmen to meet all its class size objectives. The university knows from historical data that approximately 48% of all in-province freshmen will want to live in the school dormitories, 69% of all out-of-province students will want to live in the dormitories, and there will be at most 925 dormitory rooms available for freshmen. The university also wants to make sure that it maintains high academic standards in its admissions decisions. It knows from historical data that the average SAT score for an in-province student is 945 and the average SAT score for an out-of-province student is 1,130. The university wants the entering freshman class to have an average SAT score of at least 1,050. Ghulam Ishaq Khan University is a province-supported institution, so the provincial legislature wants to make sure that the university doesn't enroll just out-of-province students because they pay more tuition and they have better SAT scores. Thus, the government has instituted a policy that no more than 63% of the entering freshman class can be out-of-province students. Develop and solve a nonlinear programming model for Ghulam Ishaq Khan University to indicate the tuition the university should charge, the total tuition, and the number of in-province and out-of-province students it can expect with these tuition rates. (13 marks) Q3. Ghulam Ishaq Khan University has increased its tuition for in-province and out-of-province students in each of the past 8 years to offset cuts in its budget allocation from the provincial legislature. The university administration always thought that the number of applications received was independent of tuition; however, drops in applications and enrollments the past 3 years have proved this theory to be wrong. University admissions officials have developed the following relationships between the number of applicants who accept admission and enter Ghulam Ishaq Khan (xi) and the cost of tuition per semester (t:) : X1 = 27,000 12t1 (in-province) X2 = 43,000 - 6t2 (out-of-province) The university would like to develop a planning model that will indicate the in-province and out-of-province tuitions, as well as the number of students that could be expected to enroll in the freshman class. The university does not have enough classroom space for more than 1,650 freshmen, and it needs at least 830 freshmen to meet all its class size objectives. The university knows from historical data that approximately 48% of all in-province freshmen will want to live in the school dormitories, 69% of all out-of-province students will want to live in the dormitories, and there will be at most 925 dormitory rooms available for freshmen. The university also wants to make sure that it maintains high academic standards in its admissions decisions. It knows from historical data that the average SAT score for an in-province student is 945 and the average SAT score for an out-of-province student is 1,130. The university wants the entering freshman class to have an average SAT score of at least 1,050. Ghulam Ishaq Khan University is a province-supported institution, so the provincial legislature wants to make sure that the university doesn't enroll just out-of-province students because they pay more tuition and they have better SAT scores. Thus, the government has instituted a policy that no more than 63% of the entering freshman class can be out-of-province students. Develop and solve a nonlinear programming model for Ghulam Ishaq Khan University to indicate the tuition the university should charge, the total tuition, and the number of in-province and out-of-province students it can expect with these tuition rates. (13 marks)