document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187637>Question 187637</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132424355/algebrahomeworkh>mathematical analysis</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The demand function for an office supply company's line of plasic rulers is p= 0.45- 0.00045q, where p is the price (in dollars) per unit when q units are demanded(per day) by consumers. Find the level of production that will minimize the mufacture's total revenue, and determine this revenue.<BR>\n" );
document.write( "Please with full details, thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140751 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=140751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The demand function for an office supply company's line of plastic rulers is<BR>\n" );
document.write( " p = 0.45 - 0.00045q, where p is the price (in dollars) per unit when q units<BR>\n" );
document.write( " are demanded(per day) by consumers.<BR>\n" );
document.write( "I think it should be:<BR>\n" );
document.write( " Find the level of production that will maximize the manufacturer's total<BR>\n" );
document.write( " revenue, and determine this revenue.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "p = 0.45 - 0.00045q<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Level of production = q<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Revenue = quantity * price<BR>\n" );
document.write( "r = q * p<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Replace p with (.45-.00045q) in the above equation and you have<BR>\n" );
document.write( "r = q * (.45-.00045q)<BR>\n" );
document.write( "r = .45q - .00045q^2<BR>\n" );
document.write( "Arrange as a quadratic equation:<BR>\n" );
document.write( "r = -.00045q^2 + .45q<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can find the value of q which gives max amt by using the eq: x = -b/(2a)<BR>\n" );
document.write( "in this equation that would be<BR>\n" );
document.write( "q = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.45%29%2F%282%2A-.00045%29 ALIGN=MIDDLE  ALT=\"%28-.45%29%2F%282%2A-.00045%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "q = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.45%29%2F%28-.00090%29 ALIGN=MIDDLE  ALT=\"%28-.45%29%2F%28-.00090%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "q = +500 units need to be produced for max revenue<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Then it says,\"and determine this revenue\"<BR>\n" );
document.write( "Substitute 500 for q in the revenue equation (r = -.00045q^2 + .45q)<BR>\n" );
document.write( "r = -.00045(500^2) + .45(500)<BR>\n" );
document.write( "r = -.00045(250000) + 225<BR>\n" );
document.write( "r = -112.5 + 225<BR>\n" );
document.write( "r = $112.5 is the max revenue and occurs when you produce 500 units<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Did this make sense to you, any questions?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );