document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042820>Question 1042820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABC Company manufactures picture frames. The weekly profit function is given by <BR>\n" );
document.write( "P(x)=-2x^2+100x-980<BR>\n" );
document.write( "1. What is the profit/loss when 20 frames are manufactured?<BR>\n" );
document.write( "2. Find the quantity that maximizes weekly profit and the maximum weekly 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 #657858 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=657858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Problem 1\r<BR>\n" );
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document.write( "Plug in x = 20\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-2x%5E2%2B100x-980 ALIGN=MIDDLE  ALT=\"P%28x%29=-2x%5E2%2B100x-980\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2820%29=-2%2820%29%5E2%2B100%2820%29-980 ALIGN=MIDDLE  ALT=\"P%2820%29=-2%2820%29%5E2%2B100%2820%29-980\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every x with 20. Now evaluate/simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2820%29=-2%28400%29%2B100%2820%29-980 ALIGN=MIDDLE  ALT=\"P%2820%29=-2%28400%29%2B100%2820%29-980\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2820%29=-800%2B2000-980 ALIGN=MIDDLE  ALT=\"P%2820%29=-800%2B2000-980\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2820%29=1200-980 ALIGN=MIDDLE  ALT=\"P%2820%29=1200-980\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2820%29=220 ALIGN=MIDDLE  ALT=\"P%2820%29=220\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When 20 frames are manufactured, the weekly profit is $220\r<BR>\n" );
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document.write( "Problem 2\r<BR>\n" );
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document.write( "In the case of y = -2x^2+100x-980, it is of the form y = ax^2 + bx + c where<BR>\n" );
document.write( "a = -2<BR>\n" );
document.write( "b = 100<BR>\n" );
document.write( "c = -980<BR>\n" );
document.write( "We will plug a = -2 and b = 100 into the formula x = -b/(2a) to find the x coordinate of the vertex.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282%2A%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282%2A%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a = -2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-100%2F%282%2A%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+-100%2F%282%2A%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b = 100\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-100%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+-100%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+25 ALIGN=MIDDLE  ALT=\"x+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the max weekly profit occurs when 25 frames are made.\r<BR>\n" );
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document.write( "Plug x = 25 into the P(x) function to find the y coordinate of the vertex.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-2x%5E2%2B100x-980 ALIGN=MIDDLE  ALT=\"P%28x%29=-2x%5E2%2B100x-980\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2825%29=-2%2825%29%5E2%2B100%2825%29-980 ALIGN=MIDDLE  ALT=\"P%2825%29=-2%2825%29%5E2%2B100%2825%29-980\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every x with 25. Now evaluate/simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2825%29=-2%28625%29%2B100%2825%29-980 ALIGN=MIDDLE  ALT=\"P%2825%29=-2%28625%29%2B100%2825%29-980\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2825%29=-1250%2B2500-980 ALIGN=MIDDLE  ALT=\"P%2825%29=-1250%2B2500-980\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2825%29=270 ALIGN=MIDDLE  ALT=\"P%2825%29=270\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The max weekly profit is $270<BR>\n" );
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