The budget for a project on voting trends includes $3400 for hiring undergraduat

Question

The budget for a project on voting trends includes $3400 for hiring undergraduate students, graduate students, and faculty members to conduct interviews on the day before an election. Each undergraduate student will conduct 22 interviews for $100. Each graduate student will conduct 28 interviews for S150. Each faculty member will conduct 32 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 f faculty members should be hired to maximize the num ber of interviews.

Explanation / Answer

Solution:

Let x = number of undergraduate students hired,

y = number of graduate students hired,

z = number of facuilty members

Objective function to maximize the number of interview

p = 22x + 28y + 32z

Constraint

x + y + z =< 19

100x + 150y + 200z =< 3400

using simplex method

Maximize p = 22x + 28y + 32z subject to
x + y + z <= 19
100x + 150y +200z <= 3400

Tableau #1
x y z s1 s2 p   
1 1 1 1 0 0 19   
100 150 200 0 1 0 3400   
-22 -28 -32 0 0 1 0

Tableau #2
x y z s1 s2 p   
0.5 0.25 0 1 -0.005 0 2
0.5 0.75 1 0 0.005 0 17   
-6 -4 0 0 0.16 1 544

Tableau #3
x y z s1 s2 p   
1 0.5 0 2 -0.01 0 4
0 0.5 1 -1 0.01 0 15   
0 -1 0 12 0.1 1 568

Tableau #4
x y z s1 s2 p   
2 1 0 4 -0.02 0 8
-1 0 1 -3 0.02 0 11   
2 0 0 16 0.08 1 576

from tableau

Optimal Solution: p = 576; x = 0, y = 8, z = 11

therefore

0 undergraduate students, 8 graduate students, and 11 faculty members should be hired to maximize the number of interviews

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