1. Consider the following notation: Let N be the number of persons to be admitted, K the set of short-listed applicants, M the set of all female applicants, R the set of all non-stanbul-region applicants, and p_i the score of applicant i. (Without loss of generality, we may assume that the scores are ordered from high to low.) Decision Variables: x_i = 1 if applicant i is selected, 0 otherwise.

Using only notation given in the question, algebraically write the following using linear statements.

1. The total number of applicants to be selected is equal to the number predetermined by the program organizers.
2. At least m percent of the selected applicants must be women.
3. At least r percent of the selected applicants must be from non-stanbul regions.
4. Write an objective to maximize the sum of the selected applicants scores.
5. Write an objective to minimize the sum of the selected applicants rankings.

Write an objective so that the last applicant selected has the best possible ranking. Hint: This is modeled as a min max objective function which is then linearized