a) University of Nairobi has enough slots for 3500 students. These slots will be allocated to three categories of students, government sponsored students, self sponsored students and international...

a) University of Nairobi has enough slots for 3500 students. These slots will be allocated to three categories of students, government sponsored students, self sponsored students and international students. The halls of residence in the University’s campuses can accommodate a maximum of 1,750 students. Half of government sponsored students, one-quarter of self sponsored students and all international students must be given places in the halls of residence. Each semester, the university gets sh. 36,000 in tuition fees for each government sponsored student, sh. 70,000 for each self sponsored student and sh. 80,000 for each international student. In order to meet its obligations and get enough funds for development, it requires at least sh. 182 million per semester.

Required

Using matrix algebra, determine the number of students in each of the three categories that the University of Nairobi should admit.