Question 1195055: The budget for a project on voting trends includes $4200 for hiring undergraduate students, graduate students, and faculty members to conduct interviews on the day before an election. Each undergraduate student will conduct 20 interviews for $100. Each graduate student will conduct 25 interviews for $150. Each faculty member will conduct 26 interviews for $200. No more than 24 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 by ikleyn(52817)   (Show Source):
You can put this solution on YOUR website! .
The budget for a project on voting trends includes $4200 for hiring undergraduate students,
graduate students, and faculty members to conduct interviews on the day before an election.
Each undergraduate student will conduct 20 interviews for $100. Each graduate student will
conduct 25 interviews for $150. Each faculty member will conduct 26 interviews for $200.
No more than 24 interviewers can be hired.
(a) How many of each type of interviewer should be hired in order to maximize the number
of interviews?
(b) What is the maximum number of interviews?
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It is a standard linear minimax problem.
Let x be the number of undergraduate students;
y be the number of graduate students
and z be the number of faculty members.
The objective function to maximize is F(x,y,z) = 20x + 25y + 26z.
There restrictions are
100x + 150y + 200z <= 4200,
x + y + z <= 24.
The solution (x,y,z) should be in integer non-negative numbers
x >= 0, y >= 0, z >= 0.
Now go to web-site https://www.zweigmedia.com/RealWorld/simplex.html
https://www.zweigmedia.com/RealWorld/simplex.html
and use free of charge solver there.
Input the objective function and the restrictions and press the "Solve" button.
It will solve this maximization problem using the simplex method.
The solver produces this answer
x = 0 undergraduate students; y = 12 graduate students; z = 12 faculty members;
p = 612 maximum number of interviews. ANSWER
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The input to the solver is shown/presented/documented below :
Maximize p = 20x + 25y + 26z subject to
100x + 150y + 200z <= 4200
x + y + z <= 24
x >= 0
y >= 0
z >= 0
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Solved.
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If you need the details of the solution (the simplex method solution procedure step by step),
the solver PROVIDES all this information for you.
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