Chapter 6.2, Problem 55E

In Problems 41-56, construct a mathematical model in the form of a linear programming problem. (The answer in the back of the book for these application problems include the model.) Then solve the problem using the simplex method. Include an interpretation of any nonzero slack variables in the optimal solution.

Opinion survey. A political scientist received a grant to fund a research project on voting trends. The budget includes $\text{\$}3,200$ for conducting door-to-door interviews on the day before an election. Undergraduate students, graduate students, and faculty members will be hired to conduct the interviews. Each undergraduate student will conduct $18$ interviews for $\text{\$}100$. Each graduate student will conduct $25$ interviews for $\text{\$}150$. Each faculty member will conduct $30$ interviews for $\text{\$}200$. Due to limited transportation facilities, no more than $20$ interviewers can be hired. How many undergraduate students, graduate students, and faculty members should be hired in order to maximize the number of interviews? What is the maximum number of interviews?