document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=64540>Question 64540</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0028251784/algebrahomeworkh>glencoe algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Bryan Starr is a 17 year old high school senior from Upper Arlington, Ohio, who started his own lawn service when he was 12. His business has grown substantially and he has been able to put away money for college, buy a truck, and invest in a new lawn equipment to keep up with the growing demand for his services. Suppose his weekly revenue R can be represented by the formula<BR>\n" );
document.write( "R= -p[squared] + 50p-125, where p is the average price he charges for each lawn.\r<BR>\n" );
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document.write( "a) Sketch a graph of the related function. Explain why it behaves like it does, considering Bryan's business.\r<BR>\n" );
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document.write( "b) Explain how Bryan could earn $400 each week.\r<BR>\n" );
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document.write( "c) What price should he charge to earn the maximum revenue? What would be his revenue?\r<BR>\n" );
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document.write( "d) Use the discriminant to find if there is a price he could charge that would make his weekly revenue $600. Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45166 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=45166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+-+%28p%5E2%29+%2B+50p+-+125 ALIGN=MIDDLE  ALT=\"R+=+-+%28p%5E2%29+%2B+50p+-+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+a%2Ap%5E2+%2B+b%2Ap+%2B+c ALIGN=MIDDLE  ALT=\"R+=+a%2Ap%5E2+%2B+b%2Ap+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -1<BR>\n" );
document.write( "b = 50<BR>\n" );
document.write( "c = -125<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-50+%2B-+sqrt%28+50%5E2-4%2A%28-1%29%2A%28-125%29%29%29%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"p+=+%28-50+%2B-+sqrt%28+50%5E2-4%2A%28-1%29%2A%28-125%29%29%29%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-50+%2B-+sqrt%28+2500+-+500%29%2F+-2%29+ ALIGN=MIDDLE  ALT=\"p+=+%28-50+%2B-+sqrt%28+2500+-+500%29%2F+-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-50+%2B-+sqrt%282000%29%29+%2F+-2%29+ ALIGN=MIDDLE  ALT=\"p+=+%28-50+%2B-+sqrt%282000%29%29+%2F+-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-50+%2B-+20%2Asqrt%285%29%29+%2F+-2%29+ ALIGN=MIDDLE  ALT=\"p+=+%28-50+%2B-+20%2Asqrt%285%29%29+%2F+-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%2825+%2B-+10%2Asqrt%285%29%29+ ALIGN=MIDDLE  ALT=\"p+=+%2825+%2B-+10%2Asqrt%285%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+25+%2B+22.361 ALIGN=MIDDLE  ALT=\"p+=+25+%2B+22.361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+47.361 ALIGN=MIDDLE  ALT=\"p+=+47.361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+25+-+22.361 ALIGN=MIDDLE  ALT=\"p+=+25+-+22.361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+2.639 ALIGN=MIDDLE  ALT=\"p+=+2.639\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This says that when Brian charges $2.64, he has no income and when<BR>\n" );
document.write( "he charges $47.36 he haas no income. This just says that if he charges too much, nobody wants to pay it. If he charges too little, he can't even make up for<BR>\n" );
document.write( "his expenses. If he charges right in between, his income is maximum.<BR>\n" );
document.write( "Because of the -1 coefficient of p^2, the parabola has a peak at he <BR>\n" );
document.write( "vertex where p = 25. Find R when p = 25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+-+%2825%5E2%29+%2B+50%2A25+-+125 ALIGN=MIDDLE  ALT=\"R+=+-+%2825%5E2%29+%2B+50%2A25+-+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+-+625+%2B+1250+-+125 ALIGN=MIDDLE  ALT=\"R+=+-+625+%2B+1250+-+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+500 ALIGN=MIDDLE  ALT=\"R+=+500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum is at (25,500) He should charge $25 to make the max income<BR>\n" );
document.write( "of $500<BR>\n" );
document.write( "sketch the graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+550%2C+300%2C+-10%2C+100%2C+-30%2C+600%2C+-%28x%5E2%29+%2B+50%2Ax+-+125%29+ ALIGN=MIDDLE  ALT=\"+graph%28+550%2C+300%2C+-10%2C+100%2C+-30%2C+600%2C+-%28x%5E2%29+%2B+50%2Ax+-+125%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "How can Brian earn $400 /wk?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+-+%28p%5E2%29+%2B+50p+-+125 ALIGN=MIDDLE  ALT=\"400+=+-+%28p%5E2%29+%2B+50p+-+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the graph, it looks like p = 14 would give about R = 400<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+-%2814%5E2%29+%2B+50%2A14+-+125 ALIGN=MIDDLE  ALT=\"R+=+-%2814%5E2%29+%2B+50%2A14+-+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+-196+%2B+700+-125 ALIGN=MIDDLE  ALT=\"R+=+-196+%2B+700+-125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+379 ALIGN=MIDDLE  ALT=\"R+=+379\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll try 14.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+-%2814.5%5E2%29+%2B+50%2A14.5+-+125 ALIGN=MIDDLE  ALT=\"R+=+-%2814.5%5E2%29+%2B+50%2A14.5+-+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+-210.25+%2B+725+-125 ALIGN=MIDDLE  ALT=\"R+=+-210.25+%2B+725+-125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+389.75 ALIGN=MIDDLE  ALT=\"R+=+389.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "my next try would be p = 15 and that gives me R = 400<BR>\n" );
document.write( "I'm not sure what the last part is.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );