document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=440190>Question 440190</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Steve owns a hotdog stand. He has found that sales of hot dogs average 42,000 hot dogs a year when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the number of hotdogs sold drop by 5000. What price per hot dog should Steve charge to realize the maximum revenue?  <BR>\n" );
document.write( " A. $1.70  <BR>\n" );
document.write( "B. $4.20  <BR>\n" );
document.write( "C. $3.35  <BR>\n" );
document.write( "D. $3.60  <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #304171 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=304171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > cent increases in price<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > = revenue<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=++%2842000+-+5000k%29%2A%28250+%2B+50k%29+ ALIGN=MIDDLE  ALT=\"+R+=++%2842000+-+5000k%29%2A%28250+%2B+50k%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in cents)<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=++%2842000+-+5000k%29%2A%28250+%2B+50k%29+ ALIGN=MIDDLE  ALT=\"+R+=++%2842000+-+5000k%29%2A%28250+%2B+50k%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+10500000+-+1250000k+%2B+2100000k+-+250000k%5E2+ ALIGN=MIDDLE  ALT=\"+R+=+10500000+-+1250000k+%2B+2100000k+-+250000k%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+-25k%5E2+%2B+85k+%2B+1050+ ALIGN=MIDDLE  ALT=\"+R+=+-25k%5E2+%2B+85k+%2B+1050+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+-5k%5E2+%2B+17k+%2B+210+ ALIGN=MIDDLE  ALT=\"+R+=+-5k%5E2+%2B+17k+%2B+210+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a parabola with a maximum, since the<BR>\n" );
document.write( "coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2 ALIGN=MIDDLE  ALT=\"k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is minus.<BR>\n" );
document.write( "The max is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-5 ALIGN=MIDDLE  ALT=\"a+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+17 ALIGN=MIDDLE  ALT=\"b+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-17%2F%28-10%29+=+1.7%0D%0ASince+%7B%7B%7Bk ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-17%2F%28-10%29+=+1.7%0D%0ASince+%7B%7B%7Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > is  the number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > cent increases in price,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50%2A1.7+=+85+ ALIGN=MIDDLE  ALT=\"+50%2A1.7+=+85+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents is the increase over $2.50 that<BR>\n" );
document.write( "Steve should allow<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.5+%2B+.85+=+3.35+ ALIGN=MIDDLE  ALT=\"+2.5+%2B+.85+=+3.35+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "He should charge $3.35 per hot dog<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "You can check this by putting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=334 ALIGN=MIDDLE  ALT=\"334\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=335 ALIGN=MIDDLE  ALT=\"335\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336 ALIGN=MIDDLE  ALT=\"336\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=++%2842000+-+5000k%29%2A%28250+%2B+50k%29+ ALIGN=MIDDLE  ALT=\"+R+=++%2842000+-+5000k%29%2A%28250+%2B+50k%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and seeing ir <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > peaks at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=335 ALIGN=MIDDLE  ALT=\"335\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );