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 $ 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 $ 100 . Each graduate student will conduct 25 interviews for $ 150 . Each faculty member will conduct 30 interviews for $ 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?
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 $ 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 $ 100 . Each graduate student will conduct 25 interviews for $ 150 . Each faculty member will conduct 30 interviews for $ 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?
Solution Summary: The author explains how the linear programming problem model is formed if a political scientist got the chance to fund the research project on voting trends.
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
$
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
$
100
. Each graduate student will conduct
25
interviews for
$
150
. Each faculty member will conduct
30
interviews for
$
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?
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