document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31366>Question 31366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> )  A brewery manufactures three types of beer - lite, regular, and dark.  Each vat of lite beer requires 6 bags of barley, 1 bag of sugar and 1 bag of hops.  Each vat of regular beer requires 4 bags of barley, 3 bag of sugar and 1 bag of hops.  Each vat of dark beer requires 2 bags of barley, 2 bag of sugar and 4 bag of hops.  Each day the brewery has 800 bags of barley, 600 bag of sugar and 300 bag of hops.  The brewery realizes a profit of $10 per vat of lite beer, $20 per vat of regular beer, and $30 per vat of dark beer.  For this linear programming problem:\r<BR>\n" );
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document.write( "(a) What are the decision variables?<BR>\n" );
document.write( "(b) What is the objective function?<BR>\n" );
document.write( "(c) What are the constraints? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18065 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><b>A brewery manufactures three types of beer - lite, regular, and dark. Each vat\r\n" );
document.write( "of lite beer requires 6 bags of barley, 1 bag of sugar and 1 bag of hops. Each\r\n" );
document.write( "vat of regular beer requires 4 bags of barley, 3 bag of sugar and 1 bag of\r\n" );
document.write( "hops. Each vat of dark beer requires 2 bags of barley, 2 bag of sugar and 4\r\n" );
document.write( "bags of hops. Each day the brewery has 800 bags of barley, 600 bag of sugar and\r\n" );
document.write( "300 bag of hops. The brewery realizes a profit of $10 per vat of lite beer, $20\r\n" );
document.write( "per vat of regular beer, and $30 per vat of dark beer. For this linear\r\n" );
document.write( "programming problem: \r\n" );
document.write( "(a) What are the decision variables?\r\n" );
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document.write( "x = the number of vats of lite beer to make each day\r\n" );
document.write( "y = the number of vats of regular beer to make each day\r\n" );
document.write( "z = the number of vats of dark beer beer to make each day\r\n" );
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document.write( "(b) What is the objective function?\r\n" );
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document.write( "Profit = $10x + $20y + $30z or\r\n" );
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document.write( "P = 10x + 20y + 30z \r\n" );
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document.write( "(c) What are the constraints?\r\n" );
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document.write( "There are six constraints (inequalities)\r\n" );
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document.write( "1.\r\n" );
document.write( ">>...Each vat of lite beer requires 6 bags of barley...<<\r\n" );
document.write( ">>...Each vat of regular beer requires 4 bags of barley...<<\r\n" );
document.write( ">>...Each vat of dark beer requires 2 bags of barley...<<\r\n" );
document.write( ">>...Each day the brewery has 800 bags of barley...<<\r\n" );
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document.write( "So this inequality is the barley constraint:  6x + 4y + 2z <= 800\r\n" );
document.write( "It ensures that the brewery does not run out of barley.\r\n" );
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document.write( "2.\r\n" );
document.write( ">>...Each vat of lite beer requires...1 bag of sugar...<<\r\n" );
document.write( ">>...Each vat of regular beer requires...3 bags of sugar...<<\r\n" );
document.write( ">>...Each vat of dark beer requires...2 bags of sugar...<<\r\n" );
document.write( ">>...Each day the brewery has...600 bags of sugar...<<\r\n" );
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document.write( "So this inequality is the sugar constraint:  1x + 3y + 2z <= 600\r\n" );
document.write( "It ensures that the brewery does not run out of sugar.\r\n" );
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document.write( "3.\r\n" );
document.write( ">>...Each vat of lite beer requires...1 bag of hops...<<\r\n" );
document.write( ">>...Each vat of regular beer requires...1 bag of hops...<<\r\n" );
document.write( ">>...Each vat of dark beer requires...4 bags of hops...<<\r\n" );
document.write( ">>...Each day the brewery has...300 bags of hops...<<\r\n" );
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document.write( "So this inequality is the hops constraint:  1x + 1y + 4z <= 300\r\n" );
document.write( "It ensures that the brewery does not run out of hops.\r\n" );
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document.write( "4.  The trivial constraint that says the amount of barley cannot be a\r\n" );
document.write( "negative number.\r\n" );
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document.write( "      x >= 0\r\n" );
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document.write( "5.  The trivial constraint that says the amount of sugar cannot be a\r\n" );
document.write( "negative number.\r\n" );
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document.write( "      y >= 0\r\n" );
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document.write( "6.  The trivial constraint that says the amount of hops cannot be a\r\n" );
document.write( "negative number.\r\n" );
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document.write( "      z >= 0\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com</PRE>  </SPAN>\n" );
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