document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173539>Question 173539</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9781567655568/algebrahomeworkh>Amsco's Preparing for the Regents Examination Mathematics B</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 18) The We Make Widgets Company manufactures widgets. They find that when they charge d dollars for each widget, their income, I(d) can be expressed by the formular I(d) = -120d^2 + 14,400d + 100. What price should they charge to maximize their income? If this price is charged, what is their maxium income?\r<BR>\n" );
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document.write( "Please can someone help me and show work, step by step? <BR>\n" );
document.write( "Thank you so much for your time.\r<BR>\n" );
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document.write( "Happy Holidays </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128434 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128434\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 18) The We Make Widgets Company manufactures widgets. They find that when they charge d dollars for each widget, their income, I(d) can be expressed by the formular I(d) = -120d^2 + 14,400d + 100. What price should they charge to maximize their income? If this price is chargeThe d coordinate = -14400/2(-120)<BR>\n" );
document.write( "d, what is their maxium income? <BR>\n" );
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document.write( "Looking at the 'a' coefficient of the given equation:<BR>\n" );
document.write( "I(d) = -120d^2 + 14400d + 100<BR>\n" );
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document.write( "We see that it is negative -- meaning that it is a parabola that is opened downward.  So, if we simply find the \"vertex\" of the equation, we'll find the \"maximum\".<BR>\n" );
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document.write( "For additional info on vertex form of a parabola:<BR>\n" );
document.write( "http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php<BR>\n" );
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document.write( "The vertex is located at:<BR>\n" );
document.write( "The d coordinate = -b/2a<BR>\n" );
document.write( "The d coordinate = -14400/2(-120)<BR>\n" );
document.write( "The d coordinate = -14400/(-240)<BR>\n" );
document.write( "The d coordinate = 60 <BR>\n" );
document.write( "What price should they charge to maximize their income?  $60<BR>\n" );
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document.write( "what is their maxium income? <BR>\n" );
document.write( "Plug it back into the original formula:<BR>\n" );
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document.write( "I(d) = -120d^2 + 14,400d + 100<BR>\n" );
document.write( "I(60) = -120(60)^2 + 14,400(60) + 100<BR>\n" );
document.write( "I(60) = -120(3600) + 14400(60) + 100<BR>\n" );
document.write( "I(60) = -432000 + 864000 + 100<BR>\n" );
document.write( "I(60) =  432000 + 100<BR>\n" );
document.write( "I(60) =  $432,100<BR>\n" );
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