Question

The budget for a project on voting trends includes ​$4400 for hiring undergraduate​ students, graduate​ students, and faculty members to conduct interviews on the day before an election. each undergraduate student will conduct 17 interviews for​ $100. each graduate student will conduct 23 interviews for​ $150. each faculty member will conduct 27 interviews for​ $200. no more than 25 interviewers can be hired. how many of each type of interviewer should be hired in order to maximize the number of​ interviews? what is the maximum number of​ interviews?]

Answer 1

To maximize the number of interviews, hire as many undergraduate students as possible within the budget and interviewer limit. With $4400 and a limit of 25 interviewers, hire 25 undergraduates to conduct a total of 425 interviews.

Step-by-step explanation:

To maximize the number of interviews conducted before an election with a budget of $4400 and a limit of 25 interviewers, we need to solve an optimization problem using linear programming. Each interviewer type has different interviews conducted per dollar spent:

Undergraduate students conduct more interviews per dollar compared to graduate students and faculty members. Therefore, to maximize interviews within the budget and limit the number of interviewers, we should hire as many undergraduate students as possible.

Let's denote the number of undergraduates, graduates, and faculty hired as U, G, and F, respectively. Our constraints are:

Solving these inequalities, we find the maximum number of undergraduates that can be hired is 25 since they require the least amount of money per interviewer ($100 each) and maximize the number of interviews per interviewer. Thus, we would hire 25 undergraduates only, yielding a total budget of $2500, well within the $4400 limit and max out the number of interviewers. This resulted in 425 interviews (25 undergraduates times 17 interviews).