document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81322>Question 81322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please helllllppp!\r<BR>\n" );
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document.write( "The price p and the quantity x sold of a certain product obey the demand equation:\r<BR>\n" );
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document.write( "x = -20p + 500   <BR>\n" );
document.write( "0 less than or equal to p which is less than or equal to 25\r<BR>\n" );
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document.write( "a) express the revenue R as a function of x<BR>\n" );
document.write( "b) what is the revenue if 20 units are sold?<BR>\n" );
document.write( "c) what quantity x maximizes revenue?  what is the maximum revenue?<BR>\n" );
document.write( "d) what price should the company charge to maximize revenue?\r<BR>\n" );
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document.write( "Thank you thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58264 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=58264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The price p and the quantity x sold of a certain product obey the demand equation: <BR>\n" );
document.write( "x = -20p + 500 <BR>\n" );
document.write( "p(x)=(500-x)/20 = 25-(1/20)x<BR>\n" );
document.write( "0 less than or equal to p which is less than or equal to 25 <BR>\n" );
document.write( "a) express the revenue R as a function of x<BR>\n" );
document.write( "Revenue(x) = (price)*(quantity)<BR>\n" );
document.write( "Rev(x) = (25-(1/20)x)(x<BR>\n" );
document.write( "Rev(x) = 25x-(1/20)x^2<BR>\n" );
document.write( "b) what is the revenue if 20 units are sold?<BR>\n" );
document.write( "Rev(20) = 25*20-(1/20)20^2<BR>\n" );
document.write( "Rev(20) = 500-20<BR>\n" );
document.write( "Rev(20) = $480<BR>\n" );
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document.write( "c) what quantity x maximizes revenue? what is the maximum revenue?<BR>\n" );
document.write( "Rev(x) is a quadratic with a=-1/20, b=25<BR>\n" );
document.write( "max occurs at x=-b/2a = [-25/(-2/20)] = [250]<BR>\n" );
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document.write( "d) what price should the company charge to maximize revenue? <BR>\n" );
document.write( "p(x) = 25-(1/20)x<BR>\n" );
document.write( "p(250) = 25-(1/20)(250)<BR>\n" );
document.write( "p(250) = 25-25/2<BR>\n" );
document.write( "p(250) = $12.50<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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