document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172100>Question 1172100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the total revenue (in dollars) from the sale of x headphones is given by R(x) = 46x and that the cost (in dollars) of manufacturing x headphones is given by C(x) = 100 − 30x + 110x2. \r<BR>\n" );
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document.write( "How many headphones (below 500) were sold if the profit was $12,650 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797055 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=797055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> revenue function is r(x) = 46x<BR>\n" );
document.write( "cost function is c(x) = 100 − 30x + 110x^2<BR>\n" );
document.write( "profit function is p(x) = r(x) - c(x) <BR>\n" );
document.write( "that makes profit function as shown on the next line.<BR>\n" );
document.write( "p(x) = 46x - (100 - 30x + 110x^2)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "p(x) = 46x - 100 + 30x - 110x^2<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "p(x) = -100 + 76x - 110x^2<BR>\n" );
document.write( "arrange the expression on the right side of the equation in descending order of degree to get:<BR>\n" );
document.write( "p(x) = -110x^2 + 76x - 100<BR>\n" );
document.write( "the graph of the profit function looks like this.\r<BR>\n" );
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document.write( "as you can see, the maximum profit is -86.873 when x = .345<BR>\n" );
document.write( "that's not even close to a profit of 12,650.<BR>\n" );
document.write( "there must be something wrong with the equations.<BR>\n" );
document.write( "please check again to see if there was an error in the presentation of this problem.<BR>\n" );
document.write( "if not, then i believe there is no way that a profit of 12,650 could be attained with these equations the way they are.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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