5. (20 points) The DLSU College Admission Test (CAT) is back. The Office the Registrar (OUR)...

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5. (20 points) The DLSU College Admission Test (CAT) is back. The Office the Registrar (OUR) is processing applications for 2023/2024. The applications fall into three categories: NCR, Regional, and International. The male-female ratios for NCR and Regional applicants are 1:1 and 3:2, respectively. For international students, the corresponding ratio is 8:1. The DLSU CAT score is an important factor in accepting new students. The statistics gathered by the university indicate that the average DLSU CAT scores for NCR, Regional and International students are 27.26. and 23. respectively. The committee on admissions has established the following desirable goals for the new freshman class: 1. 2. 3. 4. The incoming class is at least 1200 freshmen. The average DLSU CAT scores for all incoming students is at least 25. International students should account for not more than 10% of the incoming class. Regional students should account for at least 20% of the incoming class. a) Formulate the problem as a goal programming model assuming that all goals are equally important. Make sure to define all variables used in the model (16 points) b) Suppose that the DLSU OUR revised its goal regarding the intake of freshmen. Hey wish to accept exactly 1200 students for the next school year. Furthermore, the DLSU CAT score is twice as important as all remaining goals. Reformulate the problem to reflect the changes. (Just the objective function) (4 points) 5. (20 points) The DLSU College Admission Test (CAT) is back. The Office the Registrar (OUR) is processing applications for 2023/2024. The applications fall into three categories: NCR, Regional, and International. The male-female ratios for NCR and Regional applicants are 1:1 and 3:2, respectively. For international students, the corresponding ratio is 8:1. The DLSU CAT score is an important factor in accepting new students. The statistics gathered by the university indicate that the average DLSU CAT scores for NCR, Regional and International students are 27.26. and 23. respectively. The committee on admissions has established the following desirable goals for the new freshman class: 1. 2. 3. 4. The incoming class is at least 1200 freshmen. The average DLSU CAT scores for all incoming students is at least 25. International students should account for not more than 10% of the incoming class. Regional students should account for at least 20% of the incoming class. a) Formulate the problem as a goal programming model assuming that all goals are equally important. Make sure to define all variables used in the model (16 points) b) Suppose that the DLSU OUR revised its goal regarding the intake of freshmen. Hey wish to accept exactly 1200 students for the next school year. Furthermore, the DLSU CAT score is twice as important as all remaining goals. Reformulate the problem to reflect the changes. (Just the objective function) (4 points)