document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1067923>Question 1067923</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Business.  Carolyn’s Quality Candy Confectionery is famous for fudge, chocolate crème, and pralines. Its candy-making equipment is set up to make 100-pound batches at a time. Currently there is a chocolate shortage and the company can only get 120 pounds of chocolate in the next shipment. On a weeks run, the confectionery’s cooking and processing equipment is available for a total of 42 machine hours. During the same period, the employees have a total of 56 work hours available for packaging. A batch of fudge requires 20 pounds of chocolate, while a batch of cremes 25 pounds of chocolate. The cooking and processing take 120-minutes for fudge, 150 minutes for chocolate cremes, and 200 minutes for pralines. The packaging times, measuring in minutes per 1 pound box, are 1, 2 and 3, respectively, for fudge, cremes and pralines. Determine how many batches of each type of candy  the confectionery should make, assuming that the profit per 1-pound box is 50 cents on fudge, 40 cents on chocolate cremes, and 45 cents on pralines. Also find the maximum profit for the week. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683115 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</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=683115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Business.  Carolyn’s Quality Candy Confectionery is famous for fudge, chocolate crème, and pralines. <BR>\n" );
document.write( "Its candy-making equipment is set up to make 100-pound batches at a time. <BR>\n" );
document.write( "Currently there is a chocolate shortage and the company can only get 120 pounds of chocolate in the next shipment. <BR>\n" );
document.write( "On a weeks run, the confectionery’s cooking and processing equipment is available for a total of 42 machine hours. <BR>\n" );
document.write( "During the same period, the employees have a total of 56 work hours available for packaging. <BR>\n" );
document.write( "A batch of fudge requires 20 pounds of chocolate, while a batch of cremes 25 pounds of chocolate. <BR>\n" );
document.write( "The cooking and processing take 120-minutes for fudge, 150 minutes for chocolate cremes, and 200 minutes for pralines. <BR>\n" );
document.write( "The packaging times, measuring in minutes per 1 pound box, are 1, 2 and 3, respectively, for fudge, cremes and pralines. <BR>\n" );
document.write( "Determine how many batches of each type of candy  the confectionery should make, assuming that the profit per 1-pound box is <BR>\n" );
document.write( "50 cents on fudge, 40 cents on chocolate cremes, and 45 cents on pralines. <BR>\n" );
document.write( "Also find the maximum profit for the week.<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( "Let x, Y and Z be the numbers of batches for fudges, cremes and pralines, respectively.\r\n" );
document.write( "                                (Each batch is 100 pounds at a time !)\r\n" );
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document.write( "Then the profit (the objective function) is\r\n" );
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document.write( "P(X,Y,Z) = 50*100X + 40*100Y + 45*100Z   cents.\r\n" );
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document.write( "The restrictions are:\r\n" );
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document.write( " 20X +  25Y         <= 120      (restriction on chocolate amount)\r\n" );
document.write( "120X + 150Y + 200Z  <= 42*60    (restriction on 42 machine hours, written in minutes)\r\n" );
document.write( "100X + 200Y + 300Z  <= 56*60    (restriction on 56 hours packaging time, written in minutes)\r\n" );
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document.write( "The other standard restrictions are X >= 0, Y >= 0, Z >= 0.\r\n" );
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document.write( "Thus the word problem is just reduced to quantitative linear programming problem.\r\n" );
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document.write( "The next step is to input this data into the (appropriate) solver and to press the button \"SOLVE\".\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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