# Finite Math

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A political scientist has received a grant to fund a research project involving voting trends.
The budget of the grant includes \$3200 for conducting door-to-door interviews the day
be hired to conduct the interviews. Each undergraduate student will be conduct 18
interviews and be paid \$100. Each graduate student will conduct 25 interviews and be paid
\$150. Each faculty member will conduct 30 interviews and be paid \$200. Due to limited
transportation facilities, no more that 20 interviewers can be hired. One of the conditions
of the grant is that at least 50% of the interviewers must be undergraduate students. How
many undergraduate students, graduate students, and faculty members should be hired in
order to maximize the number of interviews that will be conducted?

• Finite Math - ,

If there are x undergrads, y grads, and z faculty, we have

x+y+z <= 20
100x + 150y + 200z <= 3200
x >= y+z

maximize 18x+25y+30z

Now just apply your favorite optimization tool.