document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051969>Question 1051969</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The exponent Liner offers a tour package to a group of 50 persons for a price of $300 per person but it reduces the price per person by $5 for each additional person above the 50.<BR>\n" );
document.write( "a) Does reducing the price per person to have more people join the tour give the bus company more revenue?<BR>\n" );
document.write( "b) What is the maximum number of people that will give the maximum revenue for the bus company? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667404 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 300 * 50 = 15000<BR>\n" );
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document.write( "let p be the number of people > 50, then<BR>\n" );
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document.write( "15000 + (p*(300-5p) = total revenue(R)<BR>\n" );
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document.write( "1) -5p^2 +300p + 15000 = R<BR>\n" );
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document.write( "The graph of equation 1) is a parabola that curves downward, we want the coordinates of the vertex of the parabola<BR>\n" );
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document.write( "x = -b/2a = -300 / (2(-5)) = 30<BR>\n" );
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document.write( "Substitute the value of x for p in equation 1)<BR>\n" );
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document.write( "-5(30^2) +300(30) + 15000 = 19,500<BR>\n" );
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document.write( "a) yes<BR>\n" );
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document.write( "b) max number of people is 50 + 30 = 80 people<BR>\n" );
document.write( "max revenue is $19,500<BR>\n" );
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