Finite Math
posted by Sarah .
A political scientist has received a grant to fund a research project involving voting trends.
The budget of the grant includes $3200 for conducting doortodoor interviews the day
before an election. Undergraduate students, graduate students, and faculty members will
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?

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.