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 #128437 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=128437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I always think of the maximum as being exactly between<BR>\n" );
document.write( "the 2 roots of a parabola (where it crosses the x-axis<BR>\n" );
document.write( "The quadratic formula finds the roots<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( "There is a (+) and a (-) answer, and thoses are the roots<BR>\n" );
document.write( "If you rewrite the formula like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the middle and you add<BR>\n" );
document.write( "the 2nd term to get the larger root and subtract the 2nd<BR>\n" );
document.write( "term to get the smaller root.<BR>\n" );
document.write( "So, you just have to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the maximum<BR>\n" );
document.write( "The general formula for finding roots is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation in the problem is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > replaces <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28d%29+=+-120d%5E2+%2B+14400d+%2B+100 ALIGN=MIDDLE  ALT=\"I%28d%29+=+-120d%5E2+%2B+14400d+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-120 ALIGN=MIDDLE  ALT=\"a+=+-120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+14400 ALIGN=MIDDLE  ALT=\"b+=+14400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+100 ALIGN=MIDDLE  ALT=\"c+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a+=+-14400%2F%28-240%29 ALIGN=MIDDLE  ALT=\"-b%2F2a+=+-14400%2F%28-240%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a+=+60 ALIGN=MIDDLE  ALT=\"-b%2F2a+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This says <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+60 ALIGN=MIDDLE  ALT=\"d+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28d%29 ALIGN=MIDDLE  ALT=\"I%28d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a maximum<BR>\n" );
document.write( "$60 /widget should be charged to maximize income<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The problem wants to know what that income is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28d%29+=+-120d%5E2+%2B+14400d+%2B+100 ALIGN=MIDDLE  ALT=\"I%28d%29+=+-120d%5E2+%2B+14400d+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%2860%29+=+-120%2A60%5E2+%2B+14400%2A60+%2B+100 ALIGN=MIDDLE  ALT=\"I%2860%29+=+-120%2A60%5E2+%2B+14400%2A60+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%2860%29+=+-120%2A3600+%2B+864000+%2B+100 ALIGN=MIDDLE  ALT=\"I%2860%29+=+-120%2A3600+%2B+864000+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%2860%29+=+-432000+%2B+864000+%2B+100 ALIGN=MIDDLE  ALT=\"I%2860%29+=+-432000+%2B+864000+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%2860%29+=+432100 ALIGN=MIDDLE  ALT=\"I%2860%29+=+432100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum income is $432,100<BR>\n" );
document.write( "You can check the answers by making <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > a little<BR>\n" );
document.write( "bit less, say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=59.9 ALIGN=MIDDLE  ALT=\"59.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and finding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28d%29 ALIGN=MIDDLE  ALT=\"I%28d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and a little bit more, say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60.1 ALIGN=MIDDLE  ALT=\"60.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and finding<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28d%29 ALIGN=MIDDLE  ALT=\"I%28d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > In both cases, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%28d%29 ALIGN=MIDDLE  ALT=\"I%28d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > should be <BR>\n" );
document.write( "less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432100 ALIGN=MIDDLE  ALT=\"432100\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );