document.write( "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?
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Algebra.Com's Answer #827401 by ikleyn(52818)\"\" \"About 
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\n" ); document.write( "The budget for a project on voting trends includes ​$4200 for hiring undergraduate​ students,
\n" ); document.write( "graduate​ students, and faculty members to conduct interviews on the day before an election.
\n" ); document.write( "Each undergraduate student will conduct 20 interviews for​ $100. Each graduate student will
\n" ); document.write( "conduct 25 interviews for​ $150. Each faculty member will conduct 26 interviews for​ $200.
\n" ); document.write( "No more than 24 interviewers can be hired.
\n" ); document.write( "(a) How many of each type of interviewer should be hired in order to maximize the number
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\n" ); document.write( "\n" ); document.write( "            It is a standard linear minimax problem.\r
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document.write( "Let x be the number of undergraduate students;\r\n" );
document.write( "    y be the number of      graduate students\r\n" );
document.write( "and z be the number of faculty members.\r\n" );
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document.write( "The objective function to maximize is F(x,y,z) = 20x + 25y + 26z.\r\n" );
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document.write( "There restrictions are\r\n" );
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document.write( "    100x + 150y + 200z <= 4200,\r\n" );
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document.write( "       x +    y +    z <= 24.\r\n" );
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document.write( "The solution (x,y,z) should be in integer non-negative numbers\r\n" );
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document.write( "    x >= 0, y >= 0, z >= 0.\r\n" );
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document.write( "Now go to web-site https://www.zweigmedia.com/RealWorld/simplex.html\r\n" );
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document.write( "                   https://www.zweigmedia.com/RealWorld/simplex.html\r\n" );
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document.write( "and use free of charge solver there.\r\n" );
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document.write( "Input the objective function and the restrictions and press the \"Solve\" button.\r\n" );
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document.write( "It will solve this maximization problem using the simplex method.\r\n" );
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document.write( "The solver produces this answer\r\n" );
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document.write( "   x = 0 undergraduate students;  y = 12 graduate students;  z = 12 faculty members;  \r\n" );
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document.write( "   p = 612 maximum number of interviews.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "The input to the solver is shown/presented/documented below :\r
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document.write( "Maximize p = 20x + 25y + 26z subject to\r\n" );
document.write( "100x + 150y + 200z <= 4200\r\n" );
document.write( "   x +    y +    z <= 24\r\n" );
document.write( "x >= 0  \r\n" );
document.write( "y >= 0\r\n" );
document.write( "z >= 0\r\n" );
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\n" ); document.write( "\n" ); document.write( "            Solved.\r
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\n" ); document.write( "\n" ); document.write( "If you need the details of the solution  (the simplex method solution procedure step by step),\r
\n" ); document.write( "\n" ); document.write( "the solver  PROVIDES  all this information for you.\r
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