document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208206>Question 1208206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Formulate but do not solve the problem.<BR>\n" );
document.write( "A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table.<BR>\n" );
document.write( "Sleeveless	Short-sleeve	Long-sleeve<BR>\n" );
document.write( "Cutting	8	12	14<BR>\n" );
document.write( "Sewing	22	23	28<BR>\n" );
document.write( "Packaging	5	8	8<BR>\n" );
document.write( "The cutting, sewing, and packaging departments have available a maximum of 80, 160, and 48 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? (Let x, y, and z denote the amount of sleeveless, short-sleeve, and long-sleeve, respectively.)<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 #846477 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</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=846477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Formulate but do not solve the problem.<BR>\n" );
document.write( "A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. <BR>\n" );
document.write( "The time (in minutes) required by each department to produce a dozen blouses of each type is shown <BR>\n" );
document.write( "in the following table.<BR>\n" );
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( "            Sleeveless   Short-sleeve   Long-sleeve\r\n" );
document.write( "Cutting         8            12            14\r\n" );
document.write( "Sewing         22            23            28\r\n" );
document.write( "Packaging       5             8             8\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "The cutting, sewing, and packaging departments have available a maximum of 80, 160, and 48 labor-hours, <BR>\n" );
document.write( "respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is <BR>\n" );
document.write( "operated at full capacity? (Let x, y, and z denote the amount of sleeveless, short-sleeve, and long-sleeve, <BR>\n" );
document.write( "respectively.)<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 denote the amount of sleeveless, short-sleeve, and long-sleeve, respectively, in dozens.\r\n" );
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document.write( "As you read the problem, you write three equations for three unknowns x, y and z\r\n" );
document.write( "based on require time and given time limitations\r\n" );
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document.write( "    8x + 12y + 14z =  80*60    (1)   (the cutting   department time limit, in minutes);\r\n" );
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document.write( "   22x + 23y + 28z = 160*60    (2)   (the sewing    department time limit, in minutes);\r\n" );
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document.write( "    5x +  8y +  8z =  48*60    (3)   (the packaging department time limit, in minutes).\r\n" );
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document.write( "At this point, the setup is complete.\r\n" );
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document.write( "To solve, you may use manual technique like Gauss elimination or Cramer's method.\r\n" );
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document.write( "Alternatively, you may use technology (your calculator or online solvers).\r\n" );
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document.write( "Since the problem instructs \"do not solve\", I stop at this point.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "To see many other similar solved problems, &nbsp;look into the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-word-problems-by-reducing-them-to-systems-of-linear-equations-in-three-unknowns.lesson>Solving word problems by reducing to systems of linear equations in three unknowns</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "It is intended to make your horizon wider.\r<BR>\n" );
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