Question

A.     () use Goal programming to formulate problem A, and use Maxi-Min programming to formulate problem B.

1.      () Istanbul University admission Office is processing freshman applications for the upcoming academic year. The applications fall into three categories: inside İstanbul, outside İstanbul, and international. The Measuring, Selection, and Placement Center (ÖSYM) score is an important factor in accepting new students. The statistic gathered by the university indicates that the average ÖSYM  score for inside İstanbul, outside İstanbul, and international are 80, 74, and 70 respectively. The admission committee has established the following desirable goals for the new freshman class. Keep in mind that, all goals have the same importance.

                           i.          The incoming class is at most 2000 freshman.

                          ii.          The average ÖSYM  score for all incoming students is at least 73.

                        iii.          International students constitute at least  10%  and at most 40 % of the incoming class.

                         iv.          Outside İstanbul students constitute at least 30% of the incoming class.

Answer 1

Total number of incoming students =2000

The upper limit of the number of international students =2000 *(40 / 100)=800

The lower limit of the number of international students =2000 *(10 / 100)=200

Let X be the number of international students and 200 ≤ X ≤ 800

Let Y be the number of students outside Istanbul and Y ≤ 2000 *(30 / 100) \Rightarrow Y ≤ 600

Let Z be the number of students inside Istanbul =Z ≤ 600

Average score ≤ 73