document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=236775>Question 236775</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I have looked at this prblem for almost two hours and I can't figure how to form the quadratic! Problem:<BR>\n" );
document.write( "You can see 30 widgets at $500 per year. Furthermore, you find that for each $25 decrease in price you can sell 3 more wigdets. At what price should you sell the widgets to maximize gross income and what will that price be.<BR>\n" );
document.write( "I did the long way by sub. in 25 increments and adding 3 to amount sold I came up with Gross income max = $16,875 if you sell for $375 ea. How do I work the equation to get in quadratic form from the beginning?<BR>\n" );
document.write( "Thanks - Kristen </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174192 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = \"CHANGE in number of widgets\"\r<BR>\n" );
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document.write( "income = (500 - 25x/3)(30 + x)\r<BR>\n" );
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document.write( "FOILing ___ I = 15000 + 250x - 25/3 x^2\r<BR>\n" );
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document.write( "the max is on the axis of symmetry ___ x = -b / 2a\r<BR>\n" );
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document.write( "x = -250 / 2(-25/3) = 15\r<BR>\n" );
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document.write( "selling price = 500 - 25(15)/3 = 375\r<BR>\n" );
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document.write( "widgets = 30 + 15 = 45\r<BR>\n" );
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document.write( "max income = 375 (45) = 16875 </SPAN>\n" );
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