document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=798620>Question 798620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3) The profit function for Wannamaker Trophies is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+-0.4x%5E2+%2B+fx+-+m ALIGN=MIDDLE  ALT=\"P%28x%29+=+-0.4x%5E2+%2B+fx+-+m\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  where f represents the design fee for a customer’s awards and m represents the monthly office rent.  Also, P represents the monthly profit in dollars of the small business where x is the number of awards designed in that month.  <BR>\n" );
document.write( "a) If $80 is charged for a design fee, and the monthly studio rent is $1,600; write an equation for the profit, P, in terms of x. <BR>\n" );
document.write( "b) How much is the profit when 50 award designs are sold in a month?   Answer:      <BR>\n" );
document.write( "c) How many award designs must be sold in order to maximize the profit? Show your work algebraically.  <BR>\n" );
document.write( "d) What is the maximum profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #482319 by </B><A HREF=/tutors/aboutme.mpl?userid=Finavon><B>Finavon(81)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Finavon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=482319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+-0.4x%5E2+%2B+80x+-+1600+ ALIGN=MIDDLE  ALT=\"P%28x%29+=+-0.4x%5E2+%2B+80x+-+1600+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) x=50<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=+-0.4%2A2500+%2B+4000+-+1600+=+1400 ALIGN=MIDDLE  ALT=\"P=+-0.4%2A2500+%2B+4000+-+1600+=+1400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c) <BR>\n" );
document.write( "Graph function takes 3 pairs of numbers before the equation.<BR>\n" );
document.write( "First pair define the size of the image on the screen (width then height).<BR>\n" );
document.write( "Set this to see the graph on the screen.<BR>\n" );
document.write( "Second pair are the range of values on the x axis (min then max)<BR>\n" );
document.write( "Third pair are the range of values on the y axis (min then max)<BR>\n" );
document.write( "You can calculate some vaues, but I just set these wide to see the function. Using  (-1000, 1000) for both:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-1000%2C1000%2C-1000%2C1000%2C80x-0.4x%5E2-1600%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-1000%2C1000%2C-1000%2C1000%2C80x-0.4x%5E2-1600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Inspecting the result shows that the region of interest, (in this case the values where the maximum value of y occurs) lies at higher values of y (try -500,5000). The x values can be narrowed down (try -100,400).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-100%2C400%2C-500%2C5000%2C80x-0.4x%5E2-1600%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-100%2C400%2C-500%2C5000%2C80x-0.4x%5E2-1600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Further adjustment (to -50,200,-300,2700) produces<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-50%2C200%2C-300%2C2700%2C80x-0.4x%5E2-1600%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-50%2C200%2C-300%2C2700%2C80x-0.4x%5E2-1600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Inspecting this shows the max lies around 100 sales<BR>\n" );
document.write( "d) <BR>\n" );
document.write( "Max Profit @ x=100 sales<BR>\n" );
document.write( "P=-4000+8000-1600=$2400<BR>\n" );
document.write( "That sale brought in $80 and cost 199/2.5 =$79.60<BR>\n" );
document.write( "Next sale brings in $80 but costs 201/2.5=$80.40<BR>\n" );
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