document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099679>Question 1099679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain band charges $51 per ticket for concerts when 1694 people attend. The band members realize that for every $3 increase in the ticket price 22 fewer people will attend the concert. Find a revenue function R in terms of x where x represents the number of additional $3 increases in the ticket price. \r<BR>\n" );
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document.write( "1.) R(x)=\r<BR>\n" );
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document.write( "2.) What should the ticket price be for the band to maximize its revenue? $\r<BR>\n" );
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document.write( "3.) How many people will attend the concert when the revenue is maximized? \r<BR>\n" );
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document.write( "4.) What is the band's maximum revenue? $\r<BR>\n" );
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document.write( "I'm having trouble figuring out this problem, any help is much appreciated! 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 #714197 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A certain band charges $51 per ticket for concerts when 1694 people attend.<BR>\n" );
document.write( " The band members realize that for every $3 increase in the ticket price 22 fewer people will attend the concert.<BR>\n" );
document.write( " Find a revenue function R in terms of x where x represents the number of additional $3 increases in the ticket price.<BR>\n" );
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document.write( "Let X = no. of $3 increases and no. of 22 ticket decreases<BR>\n" );
document.write( " 1.) R(x)= (1694-22x)*(51+3X)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "R(x) = 86394 + 5082x - 1122x - 66x^2<BR>\n" );
document.write( "R(x) = -66x^2 + 3960x + 86394 is the revenue function<BR>\n" );
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document.write( " 2.) What should the ticket price be for the band to maximize its revenue?<BR>\n" );
document.write( "This is a quadratic equation, the maximum will occur on the axis of symmetry<BR>\n" );
document.write( "Find this using x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3960%29%2F%282%2A-66%29 ALIGN=MIDDLE  ALT=\"%28-3960%29%2F%282%2A-66%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +30 ea $3 price increases for max revenue, therefore<BR>\n" );
document.write( "30($3) + $51 = $141 will be he ticket price for max revenue<BR>\n" );
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document.write( " 3.) How many people will attend the concert when the revenue is maximized?<BR>\n" );
document.write( "1694 - 30(22) = 1034 people will attend<BR>\n" );
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document.write( " 4.) What is the band's maximum revenue? $<BR>\n" );
document.write( "1034 * $141 = $145,794  </SPAN>\n" );
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