document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178936>Question 1178936</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.A firm produces headphone in two qualities, Basic (B) and Premium (P). For the coming year, the estimated output of B is 50% higher than that of P. The profit per unit sold is $300 for P and $200 for B. If the profit target is $180 000 over the next year, how much of each of the two qualities must be produced? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808408 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=808408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b = number of basic headphones<BR>\n" );
document.write( "p = number of premium headphones.\r<BR>\n" );
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document.write( "profit for basic = 200 each.<BR>\n" );
document.write( "profit for premium = 300 each.\r<BR>\n" );
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document.write( "number of basic headphones made is 1.5 times the number of premium headphones made.\r<BR>\n" );
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document.write( "total profit target is 180,000.\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:\r<BR>\n" );
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document.write( "b = 1.5 * p<BR>\n" );
document.write( "200 * b + 300 * p = 180,000\r<BR>\n" );
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document.write( "in the second equation, replace b with 1.5 * p to get:<BR>\n" );
document.write( "200 * (1.5 * p) + 300 * p = 180,000<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "300 * p + 300 * p = 180,000<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "600 * p = 180,000<BR>\n" );
document.write( "solve for p to get:<BR>\n" );
document.write( "p = 180,000 / 600 = 300<BR>\n" );
document.write( "since b = 1.5 * p, then b = 1.5 * 300 = 450.\r<BR>\n" );
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document.write( "450 * 200 profit for basic headphone plus + 300 * 300 profit for premium headphone = 180,000 total profit.<BR>\n" );
document.write( "1.5 * 300 premium headphones = 450 basic headphones.\r<BR>\n" );
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document.write( "the basic requirements of the problem are satisfied.\r<BR>\n" );
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document.write( "the solution is that the firm needs to produce and sell 450 basic headphones and 300 premium headphones to make a profit of 180,000,<BR>\n" );
document.write( " </SPAN>\n" );
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