As rush coordinator for the Alpha Beta Chi (ABC) sorority, Kim Grant asked each pledge to identify five existing members of ABC whom she would most like to have as a big sister. Kim then asked the pledges to rank order these potential big sisters from 5 down to 1, where 5 represents the person they most want as a big sister, 4 represents the next choice, and so on. These rankings are summarized in the following table:

After much consideration, Kim decides that this problem is similar to some of the problems she encountered in a business analytics class she took during her sophomore year. She knows that every pledge must be assigned a big sister, and each potential big sister can be assigned no more than one pledge. Ideally, Kim wants to assign each pledge to the big sister to whom she gave a ranking of 5. The sum of the rankings for such an assignment is 25 because each of the 5 pledges would be assigned to the big sister they ranked as number 5. But in the previous table, that would involve assigning pledges 2 and 4 to the same big sister, which is not allowable. Kim figures that the next best strategy is to determine the assignment that maximizes the sum of the rankings.
a. Create a spreadsheet model for Kim's problem and solve it.
b. Which pledges should be assigned to which big sisters?
c. Can you think of another objective that Kim might use to solve her problem?

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Big Sisters Pledges 1 2 3 45 6 78 9 10 1 12 13 14 15 2 2