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Question 1 (10 points) From Fred Buckley, Marty Lewinter A Friendly Introduction to Graph Theory Ann, Dan, Fan, Nan, and Van are applying for jobs a,b,c,d, and e. Ann is qualified for a, b, and c; Dan for b, d, and e; Fan for b and c; Nan for c and d; and Van for b. Find a maximum matching to create maximum employment.
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Answer #1

If we draw a graph for this problem,

For Job A only Ann is qualified

For Job B Ann, Dan, Fan, Van are qualified

For Job C Ann, Fan, Nan are qualified

For Job D Dan, Nan are qualified

For Job E only Dan is qualified

so maximum matching to create maximum employment will be Job B, as it has maximum people who are qualified.

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