document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162430>Question 1162430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A textile manufacturer makes blankets and sells them for $25 each. The cost, in dollars, of making x blankets is given by the formula:  Cost=c(x)=5000+4x+0.001x^2.<BR>\n" );
document.write( "Find the number of blankets that the manufacturer should produce in order to maximize its profit.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786230 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=786230\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cost is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2B4x%2B0.001x%5E2 ALIGN=MIDDLE  ALT=\"5000%2B4x%2B0.001x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The sale price is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x ALIGN=MIDDLE  ALT=\"25x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore, the profit is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x+-+%285000%2B4x%2B0.001x%5E2%29 ALIGN=MIDDLE  ALT=\"25x+-+%285000%2B4x%2B0.001x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify the profit:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x+-+5000+-+4x+-+0.001x%5E2 ALIGN=MIDDLE  ALT=\"25x+-+5000+-+4x+-+0.001x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.001x%5E2+%2B+21x+-+5000 ALIGN=MIDDLE  ALT=\"-0.001x%5E2+%2B+21x+-+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To find the maximum profit, use the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where b = 21 and a = -0.001.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-21%29%2F%282%28-0.001%29%29 ALIGN=MIDDLE  ALT=\"%28-21%29%2F%282%28-0.001%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-21%29%2F%28-0.002%29 ALIGN=MIDDLE  ALT=\"%28-21%29%2F%28-0.002%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10500<BR>\n" );
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document.write( "<b>The maximum profit is reached when the manufacturer makes 10,500 blankets.</b><BR>\n" );
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document.write( "Check it:<BR>\n" );
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document.write( "When the manufacturer makes 10,500 blankets, the profit is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.001x%5E2+%2B+21x+-+5000 ALIGN=MIDDLE  ALT=\"-0.001x%5E2+%2B+21x+-+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.001%2810500%29%5E2+%2B+21%2810500%29+-+5000 ALIGN=MIDDLE  ALT=\"-0.001%2810500%29%5E2+%2B+21%2810500%29+-+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 105250.<BR>\n" );
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document.write( "When the manufacturer makes 10,499 blankets, the profit is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.001x%5E2+%2B+21x+-+5000 ALIGN=MIDDLE  ALT=\"-0.001x%5E2+%2B+21x+-+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.001%2810499%29%5E2+%2B+21%2810499%29+-+5000 ALIGN=MIDDLE  ALT=\"-0.001%2810499%29%5E2+%2B+21%2810499%29+-+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 105249.999<BR>\n" );
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document.write( "When the manufacturer makes 10,501 blankets, the profit is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.001x%5E2+%2B+21x+-+5000 ALIGN=MIDDLE  ALT=\"-0.001x%5E2+%2B+21x+-+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.001%2810501%29%5E2+%2B+21%2810501%29+-+5000 ALIGN=MIDDLE  ALT=\"-0.001%2810501%29%5E2+%2B+21%2810501%29+-+5000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 105249.999 </SPAN>\n" );
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