document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199320>Question 1199320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bài 7/557) A food producer uses two processing plants, P1 and P2, that<BR>\n" );
document.write( "operate 7 days a week. After processing, beef is graded into high-, mediumand low-quality foodstuf s. High-quality beef is sold to butchers, mediumquality beef is used in supermarket ready-meals and the low-quality beef is<BR>\n" );
document.write( "used in dog food. The producer has contracted to provide 120 kg of high-,<BR>\n" );
document.write( "80 kg of medium- and 240 kg of low-quality beef each week. It costs $4000<BR>\n" );
document.write( "per day to run plant P1 and $3200 per day to run plant P2. Each day P1<BR>\n" );
document.write( "processes 60 kg of high-quality beef, 20 kg of medium-quality beef and 40kg of low-quality beef. The corresponding quantities for P2 are 20 kg, 20 kg<BR>\n" );
document.write( "and 120 kg, respectively. How many days each week should the plants be<BR>\n" );
document.write( "operated to fulfi l the beef contract most economically? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833149 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52800)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A food producer uses two processing plants, P1 and P2, that<BR>\n" );
document.write( "operate 7 days a week. After processing, beef is graded into high-, medium and low-quality food stuf s. <BR>\n" );
document.write( "High-quality beef is sold to butchers, medium quality beef is used in supermarket, ready-meals and the low-quality beef <BR>\n" );
document.write( "is used in dog food. <BR>\n" );
document.write( "The producer has contracted to provide 120 kg of high-, 80 kg of medium- and 240 kg of low-quality beef each week. <BR>\n" );
document.write( "It costs $4000 per day to run plant P1 and $3200 per day to run plant P2. <BR>\n" );
document.write( "Each day P1 processes 60 kg of high-quality beef, 20 kg of medium-quality beef and 40kg of low-quality beef. <BR>\n" );
document.write( "The corresponding quantities for P2 are 20 kg, 20 kg and 120 kg, respectively. <BR>\n" );
document.write( "How many days each week should the plants be operated to fulfil the beef contract most economically?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "x = days for plant P1;\r\n" );
document.write( "y = days for plant P2.\r\n" );
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document.write( "Objective function to minimize is\r\n" );
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document.write( "    p(x,y) = 4000x + 3200y  dollars.\r\n" );
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document.write( "Constraints\r\n" );
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document.write( "    60x + 20y >= 120   (high-quality beef, in kilograms)\r\n" );
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document.write( "    20x + 20y >=  80   (medium-quality beef)\r\n" );
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document.write( "    40x + 120y >= 240  (low-quality beef)\r\n" );
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document.write( "     0 <= x <= 7;  0<= y <= 7   (days to work)\r\n" );
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document.write( "    \r\n" );
document.write( "Now go to the site  https://www.zweigmedia.com/RealWorld/simplex.html\r\n" );
document.write( "and use the free of charge solver there.\r\n" );
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document.write( "The input to the solver is shown/presented/documented below :\r\n" );
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document.write( "Minimize p = 4000x + 3200y\r\n" );
document.write( "60x + 20y >= 120 \r\n" );
document.write( "20x + 20y >=  80\r\n" );
document.write( "40x + 120y >= 240\r\n" );
document.write( "x >= 0\r\n" );
document.write( "x <= 7\r\n" );
document.write( "y >= 0\r\n" );
document.write( "y <= 7\r\n" );
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document.write( "Copy-paste it to the solver.\r\n" );
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document.write( "It will solve this minimization problem using the Linear Programming method / (the \"simplex method\").\r\n" );
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document.write( "The solver produces this solution (this answer)\r\n" );
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document.write( "   x = 1 day;  y = 3 days;  p = $13600.    <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "At this point, &nbsp;the solution is complete.\r<BR>\n" );
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document.write( "---------------\r<BR>\n" );
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document.write( "There are several ways to solve the problem.\r<BR>\n" );
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document.write( "For example, since the problem is &nbsp;2D &nbsp;(for &nbsp;2 &nbsp;unknown variables), &nbsp;graphics method does work.\r<BR>\n" );
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document.write( "On solving using graphics method, &nbsp;see the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/misc/Solving-minimax-problems-by--the-Linear-Programming-method.lesson>Solving minimax problems by the Linear Programming method</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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