document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189901>Question 1189901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7. The top two dolls that a toy manufacturer makes are called Baby Wiggles and<BR>\n" );
document.write( "Sleepy Baby. To make a case of Baby Wiggles takes 10 units of raw material<BR>\n" );
document.write( "and I unit of time to assemble. To make a case of Sleepy Baby takes 6 units of<BR>\n" );
document.write( "raw material and 2 units of time to assemble. On a given day the manufacturer<BR>\n" );
document.write( "has at most 300 units of raw material and 44 units of time. If the manufacturer<BR>\n" );
document.write( "makes a profit of $170 on each case of Baby Wiggles and $140 on each case<BR>\n" );
document.write( "of Sleepy Baby, how many cases of each type of doll should the manufacturer<BR>\n" );
document.write( "make in order to maximize profit?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821411 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = the number of cases of baby wiggles<BR>\n" );
document.write( "y = the number of cases of sleepy baby.\r<BR>\n" );
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document.write( "baby wiggles takes 10 units of raw material and 1 unit of time to assemble.<BR>\n" );
document.write( "sleepy baby takes 6 units of raw material and 2 units of time to assmble.\r<BR>\n" );
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document.write( "on a given day, the manufacturer has at most 300 units of raw materials and 44 units of time available.\r<BR>\n" );
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document.write( "the manufacturer makes a profit of 170 on each case of baby wiggles and 140 on each case of sleepy baby.\r<BR>\n" );
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document.write( "your constraint inequalities are:\r<BR>\n" );
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document.write( "10x + 6y <= 300<BR>\n" );
document.write( "x + 2y <= 44<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "your objective function is:\r<BR>\n" );
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document.write( "profit = 170 * x + 140 * y\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would graph the opposite of the constraints and then evaluate the objective function at the corner poinjts of the feasible region.\r<BR>\n" );
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document.write( "the feasible region is the area on the graph that is not shaded.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "all constraints need to be met.<BR>\n" );
document.write( "at the maximum profit point of (24,10), .....<BR>\n" );
document.write( "10x + 6y = 240 + 60 = 300 which is <= 300<BR>\n" );
document.write( "x + 2y = 24 + 20 = 44 which is <= 44.<BR>\n" );
document.write( "this confirms all the constraints are met.\r<BR>\n" );
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document.write( "your maximum profit is when 24 cases of baby wiggles and 10 cases of sleepy baby are manufactured and sold.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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