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# 1.Consider the following notation: Let N be the number of

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*= 1 if applicant

_{i}*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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