document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446766>Question 446766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An amusement park has been charging $12 per person for admission and averaging 1000 patrons per day. the directors of the park are considering a $2 increase in the price for next season . They have calculated that for each $2 in increase they will probably lose 100 patrons per day. What should be the ideal admission fee for the greatest income on an average day . Write an equation to model the situation and draw a graph of the situation to justify your answer.\r<BR>\n" );
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document.write( "So I got the ideal price to be $16 <BR>\n" );
document.write( "The equation is what i'm not sure of , I got (x-16)^2= p(y-12800) Not sure on how to find P , Also not sure if the equation is correct </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307796 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=307796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An amusement park has been charging $12 per person for admission and averaging 1000 patrons per day.<BR>\n" );
document.write( " the directors of the park are considering a $2 increase in the price for next season .<BR>\n" );
document.write( " They have calculated that for each $2 in increase they will probably lose 100 patrons per day.<BR>\n" );
document.write( " What should be the ideal admission fee for the greatest income on an average day<BR>\n" );
document.write( " . Write an equation to model the situation and draw a graph of the situation to justify your answer.<BR>\n" );
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document.write( "I think you are right, but I would do it this way.<BR>\n" );
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document.write( "Let x = no. of $2 increases and no. of 100 patron decreases<BR>\n" );
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document.write( "Income = price * no. patrons<BR>\n" );
document.write( "f(x) = (12+2x)*(1000-100x)<BR>\n" );
document.write( "Foil<BR>\n" );
document.write( "f(x) = 12000 - 1200x + 2000x - 200x^2<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "f(x) = -200x^2 + 800x + 12000, is the equation<BR>\n" );
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document.write( "The greatest income occurs when x = the axis of symmetry, x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-800%29%2F%282%2A-200%29 ALIGN=MIDDLE  ALT=\"%28-800%29%2F%282%2A-200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +2<BR>\n" );
document.write( "Therefore max income when<BR>\n" );
document.write( "12+2(2) = $16 is the price (which you got)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "1000 - 2(100) = 800 patrons at that price<BR>\n" );
document.write( "Max income<BR>\n" );
document.write( "16 * 800 = $12,800 <BR>\n" );
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document.write( "To graph this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+8%2C+-2000%2C+18000%2C+-200x%5E2%2B800x%2B12000%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-2000%2C+18000%2C+-200x%5E2%2B800x%2B12000%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can confirm this, substitute 2 in the equation to find f(x) = 12,800 </SPAN>\n" );
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