document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137592>Question 1137592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this question. <BR>\n" );
document.write( "The demand function for a new DVD is p(x)=-2.5x+17.5 where p(x) represents the selling price, in thousands of dollars, and x is the number of DVDs sold, in thousands. <BR>\n" );
document.write( "a) Determine the revenue function.<BR>\n" );
document.write( "b) Determine the maximum revenue.<BR>\n" );
document.write( "c) Determine the number of DVDs that need to be sold to reach the maximum revenue. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755462 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28x%29=-2.5x%2B17.5 ALIGN=MIDDLE  ALT=\"+p%28x%29=-2.5x%2B17.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29 ALIGN=MIDDLE  ALT=\"p%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the selling price, in thousands of dollars, and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of DVDs sold, in thousands. \r<BR>\n" );
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document.write( "a) Determine the revenue function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Revenue+=+Price+%2A+Quantity ALIGN=MIDDLE  ALT=\"+Revenue+=+Price+%2A+Quantity\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=p%28x%29%2Ax ALIGN=MIDDLE  ALT=\"R%28x%29=p%28x%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=%28-2.5x%2B17.5%29x ALIGN=MIDDLE  ALT=\"R%28x%29=%28-2.5x%2B17.5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-2.5x%5E2%2B17.5x ALIGN=MIDDLE  ALT=\"R%28x%29=-2.5x%5E2%2B17.5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) Determine the maximum revenue.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-2.5x%5E2%2B17.5x ALIGN=MIDDLE  ALT=\"R%28x%29=-2.5x%5E2%2B17.5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >............complete square to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the vertex of a quadratic parabola is the highest or lowest point, the maximum or minimum \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-2.5%28x%5E2-7x%29 ALIGN=MIDDLE  ALT=\"R%28x%29=-2.5%28x%5E2-7x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-2.5%28x%5E2-7x%2Bb%5E2%29-%28-2.5%29b%5E2 ALIGN=MIDDLE  ALT=\"R%28x%29=-2.5%28x%5E2-7x%2Bb%5E2%29-%28-2.5%29b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-2.5%28x%5E2-7x%2Bb%5E2%29%2B2.5b%5E2 ALIGN=MIDDLE  ALT=\"R%28x%29=-2.5%28x%5E2-7x%2Bb%5E2%29%2B2.5b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7%2F2=3.5 ALIGN=MIDDLE  ALT=\"b=7%2F2=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-2.5%28x%5E2-7x%2B3.5%5E2%29%2B2.5%2A3.5%5E2 ALIGN=MIDDLE  ALT=\"R%28x%29=-2.5%28x%5E2-7x%2B3.5%5E2%29%2B2.5%2A3.5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-2.5%28x-3.5%29%5E2%2B30.625 ALIGN=MIDDLE  ALT=\"R%28x%29=-2.5%28x-3.5%29%5E2%2B30.625\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the maximum is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5 ALIGN=MIDDLE  ALT=\"3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30.625 ALIGN=MIDDLE  ALT=\"30.625\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "or, this way:\r<BR>\n" );
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document.write( "derivate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29 ALIGN=MIDDLE  ALT=\"R%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%2Fdx=-2.5%2A2x%2B17.5 ALIGN=MIDDLE  ALT=\"R%2Fdx=-2.5%2A2x%2B17.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%2B17.5=0 ALIGN=MIDDLE  ALT=\"-5x%2B17.5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=17.5 ALIGN=MIDDLE  ALT=\"5x=17.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.5 ALIGN=MIDDLE  ALT=\"x=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%283.5%29 ALIGN=MIDDLE  ALT=\"r%283.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%283.5%29=-2.5%2A3.5%5E2%2B17.5%2A3.5 ALIGN=MIDDLE  ALT=\"R%283.5%29=-2.5%2A3.5%5E2%2B17.5%2A3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%283.5%29=-30.625%2B61.25 ALIGN=MIDDLE  ALT=\"R%283.5%29=-30.625%2B61.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%283.5%29=30.625 ALIGN=MIDDLE  ALT=\"R%283.5%29=30.625\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=maximum ALIGN=MIDDLE  ALT=\"maximum\"   DISABLED_style= \"max-width:90%; height:auto;\" > revenue \r<BR>\n" );
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document.write( "c) Determine the number of DVDs that need to be sold to reach the maximum revenue. <BR>\n" );
document.write( " <BR>\n" );
document.write( "since the maximum is at vertex (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5 ALIGN=MIDDLE  ALT=\"3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30.625 ALIGN=MIDDLE  ALT=\"30.625\"   DISABLED_style= \"max-width:90%; height:auto;\" >), the number of DVDs that  need to be sold to reach the maximum revenue is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.5 ALIGN=MIDDLE  ALT=\"x=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, in thousands, the number of DVDs that need to be sold to reach the maximum revenue is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3500 ALIGN=MIDDLE  ALT=\"3500\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );