document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202521>Question 1202521</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The top two dolls that a toy manufacturer makes are called Baby Wiggles and Sleepy Baby.To makes a case of Baby Wiggles takes 5 units of raw material and 1 unit of time to assemble.To make a case pf Sleepy Baby takes 3 units of raw material and 2 units of time to assemble.On a given day the manufacturer has at most 150 units of raw material and  44 units of time.If the manufacturer makes a profit of RM120 on each case of Baby Wiggles and RM100 on each case of Sleepy Baby,how many cases of each type of doll should the manufacturer 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 #837404 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=837404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of cases of baby wiggles.<BR>\n" );
document.write( "y = number of cases of sleepy baby.\r<BR>\n" );
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document.write( "objective function is profit = 120x + 100y\r<BR>\n" );
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document.write( "constraint functions are:<BR>\n" );
document.write( "5x + 3y <= 150 for raw material.<BR>\n" );
document.write( "1x + 2y <= 44 for units of time.<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "using the desmos.com calculator at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a>, you would graph the opposite of the constraint inequalities.<BR>\n" );
document.write( "the area of the graph not shaded is your region of feasibility.<BR>\n" );
document.write( "the corner points of this region would contain the maximum profit solution.<BR>\n" );
document.write( "you would evaluate the objective function at each of these corner points to obtain the maximum profit.\r<BR>\n" );
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document.write( "the graph looks like this.\r<BR>\n" );
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document.write( "profit = 120x + 100y<BR>\n" );
document.write( "at (0,22), profit is equal to 2200<BR>\n" );
document.write( "at (24,10), profit is equal to 3880<BR>\n" );
document.write( "at (30,0), profit is equal to 3600\r<BR>\n" );
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document.write( "maximum profit is at (24,10).\r<BR>\n" );
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document.write( "all constraints need to be satisfied at that point.\r<BR>\n" );
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document.write( "constraint functions are:<BR>\n" );
document.write( "5x + 3y <= 150 for raw material becomes 5*24 + 3 * 3 * 10 = 150.<BR>\n" );
document.write( "1x + 2y <= 44 for units of time becomes 24 + 2*10 = 44.<BR>\n" );
document.write( "x >= 0 and y >= 0.<BR>\n" );
document.write( "all constraints are satisfied.\r<BR>\n" );
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document.write( "your solution is 24 cases of baby wiggles and 10 cases of sleepy baby will maximize profit.\r<BR>\n" );
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