Question

stue. VULP LES Question Help 6.2.55-SS The budget for a project on voting trends includes $3000 for hiring undergraduate students, graduate students, and faculty members to conduct interviews on the day before an election Each undergraduate student will conduct 23 interviews for $100. Each graduate student will conduct 27 interviews for $150 Each faculty member will conduct 30 interviews for $200. No more than 19 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 undergraduate students, graduate students, and faculty members should be hired to maximize the number of interviews.

Answer 1

Let x undergraduate students, y graduate students, z faculty members should be hired and let A be the total number of interviews.

Then, x undergraduate students will conduct (x*23) = 23x interviews

y graduate students will conduct (y*27) = 27y interviews

z faculty members will conduct (z*30) = 30z interviews

And, the cost for conducting interviews by x undergraduate students is = $(x*100) = $100x

the cost for conducting interviews by y graduate students is = $(y*150) = $150y

the cost for conducting interviews by z faculty members is = $(z*200) = $200z

Now, the total number of interviews is = (23x+27y+30z)

and, the total number of interviewers is = (x+y+z)

and, the total cost for conducting interviews is = $(100x+150y+200z)

Then, the linear programming problem becomes,

Maximize A = 23x+27y+30z

Subject to 100x+150y+200z $\leq$ 3000

x+y+z $\leq$ 19

x, y, z $\geq$ 0

We are going to solve this problem using EXCEL.

Solving we get

x = 0, y = 16, z = 3

Now, Amax = 23*0+27*16+30*3 = 0+432+90 = 522

Therefore, 0 undergraduate students, 16 graduate students, 3 faculty members should be hired to maximize the number of interviews and the maximum number of interviews is 522.