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-İstanbul-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.

• The total number of applicants to be selected is equal to the number predetermined by the program organizers.
• At least m percent of the selected applicants must be women.
• At least r percent of the selected applicants must be from non-İstanbul regions.
• Write an objective to maximize the sum of the selected applicants’ scores.
• 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.

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