document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032512>Question 1032512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> GoQuik Dinners makes meals for people on the go. The company models their profit with the function P = -2x^2 + 14x - 20, where x is the number of meals produced in hundreds, and P is the company's profits, in thousands \r<BR>\n" );
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document.write( "a) How many meals must be produced for the company to break even?<BR>\n" );
document.write( "b) How many meals does GoQuik need to produce to maximize their profit?<BR>\n" );
document.write( "c) What is the maximum profit they could earn?\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647270 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) To break even, P = 0...we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2+%2B+14x+-+20+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2+%2B+14x+-+20+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+7x+%2B+10+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+7x+%2B+10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x-5%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x-5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Thus they break even at 200 meals and at 500 meals.<BR>\n" );
document.write( "b)  To maximize profit, we take the derivative and set it equal to zero, so that<BR>\n" );
document.write( "P' = -4x + 14 = 0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = 3.5 = 350 meals<BR>\n" );
document.write( "c)  To find out what that profit is, we plug 3.5 in for x in the original and get<BR>\n" );
document.write( "P(3.5) = -2(3.5)^2 + 14(3.5) - 20 = 4.5 = $4500 </SPAN>\n" );
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