Scenario You are studying Human Sciences, administration profile. When you have completed your college diploma, several paths will open to you in your university career. It is not uncommon to see students with this college education opt for a university management program. The majority of Quebec universities offer such a training sector, although each of them has its particularities. For example, the School of Management Sciences (ESG), affiliated with UQAM, offers various training courses including bachelor's degrees in administration, economics and accounting sciences. At the cole des Hautes tudes Commerciales (HEC), affiliated with the University of Montreal, the main program is a bachelor's degree in business administration, offering, among other things, specializations in economics or accounting. In Quebec, Laval University also offers this type of training. The Faculty of Administrative sciences offers, just like at HEC, the baccalaureate in business administration with its specialized paths. Question 2 Although making a profit is not the primary motivation for university managers, they still face high expenses. Whether to pay its teaching staff and other employees, maintain its buildings or to support numerous research projects, the university must generate a certain income to maintain the quality of the training given there. One of the main sources of income is tuition fees paid by students. Let's consider again the administration, economics and accounting programs at UQAM. During the admission process, the university must respect certain constraints: Annually, the number of new students admitted to the three programs combined must not exceed 3,500. Additionally, due to limited space, the economics and accounting departments are located in the same university building, so they cannot admit more than 2,000 new students under their roof. Furthermore, the number of students admitted to administration never exceeds twice the number of students admitted to accounting. The following table presents the results of a study carried out by financial services and the UQAM registrar's office. The table gives the average amount that a student will have to pay in tuition fees during the duration of their baccalaureate depending on the program of study. Study programme Bachelor of Administration Bachelor of Economics Bachelor of Accounting Average amount paid in rights tuition (in thousands of dollars) 7,5 8,0 6,5 a) a) Determine the number of students from each program that the university should admit if it wants to maximize its tuition revenue, while respecting the constraints explained above. b) In the first octant of the Cartesian space, illustrate the constraint that the number of new students admitted to the three programs combined must not exceed 3,500.