document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205168>Question 1205168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Emilia manages a company that makes and sells two kinds of speakers, the Boomer and the Rocker. Each Boomer takes 10 hours to create the plastic parts, 5 hours to create the electronics, and 6 hours for assembly. Each Rocker requires 6 hours to create the plastic parts, 6 hours to create the electronics, and 4 hours for assembly. The factory can handle a maximum of 3020 hours to create the plastic parts, 1848 hours to create the electronics, and 1840 hours for assembly each week. If each Boomer generates $8 in revenue, and each Rocker generates $11, how many of each of the speakers should Emilia have the company make and sell each week to earn the most revenue?<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 #841823 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=841823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of boomer speakers.<BR>\n" );
document.write( "y = number of rocker speakers.\r<BR>\n" );
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document.write( "plastic parts:<BR>\n" );
document.write( "10x + 6y <= 3020<BR>\n" );
document.write( "electronics:<BR>\n" );
document.write( "5x + 6y <= 1848<BR>\n" );
document.write( "assembly:<BR>\n" );
document.write( "6x + 4y <= 1840<BR>\n" );
document.write( "revenue:<BR>\n" );
document.write( "8x + 11y = objective function to maximize.\r<BR>\n" );
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document.write( "using the desmos.com/calculator, you would:<BR>\n" );
document.write( "graph the opposite of the inequalities.<BR>\n" );
document.write( "the area that is not shaded is the region of feasibility.<BR>\n" );
document.write( "the corner points of that region are where the maximum revenue lies.\r<BR>\n" );
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document.write( "the graph looks like this:\r<BR>\n" );
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document.write( "the maximum revenue is at the point (0,308) where the revenue = 8 * 0 +  11 * 308 = 3388.<BR>\n" );
document.write( "all the constraints are satisfied.<BR>\n" );
document.write( "plastic parts:<BR>\n" );
document.write( "10x + 6y = 10 * 0 + 6 * 308 = 1848 <= 3020<BR>\n" );
document.write( "electronics:<BR>\n" );
document.write( "5x + 6y = 5 * 0  + 6 * 308 = 1848 <= 1848<BR>\n" );
document.write( "assembly:<BR>\n" );
document.write( "6x + 4y  = 6 * 0 + 4 * 308 = 1232 <= 1840\r<BR>\n" );
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