document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=959010>Question 959010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Woods Limited manufactures and sells x small patio tables each day. The daily cost of production is modeled as C(x) = 3x2 + 1500, and the revenue produced each day is modeled as R(x) = 180x.  Suppose the company is limited by time to producing at least 30 tables every day.  What is the break-even point?  If the company sells 45 tables, then what is the profit?   How many tables must the company produce in order to get a profit of $1,125? What happen if the company produces 58 tables?\r<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 #586132 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=586132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Woods Limited manufactures and sells <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > small patio tables each day. <BR>\n" );
document.write( "The daily cost of production is modeled as <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29+=+3x%5E2+%2B+1500 ALIGN=MIDDLE  ALT=\"C%28x%29+=+3x%5E2+%2B+1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the revenue produced each day is modeled as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29+=+180x ALIGN=MIDDLE  ALT=\"R%28x%29+=+180x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Suppose the company is limited by time to producing at least <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" > (at least means &#8805;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" >)tables every day.<BR>\n" );
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document.write( "1. What is the break-even point? <BR>\n" );
document.write( "to find it set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29+=+C%28x%29 ALIGN=MIDDLE  ALT=\"R%28x%29+=+C%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then solve the resulting quadratic equation  <BR>\n" );
document.write( "he break-even point occurs when <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%5E2+%2B+1500=180x ALIGN=MIDDLE  ALT=\"+3x%5E2+%2B+1500=180x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%5E2+-180x%2B+1500=0 ALIGN=MIDDLE  ALT=\"+3x%5E2+-180x%2B+1500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......simplify, divide all terms by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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+-60x%2B+500=0 ALIGN=MIDDLE  ALT=\"+x%5E2+-60x%2B+500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ........use quadratic formula\r<BR>\n" );
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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;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-60%29%2B-+sqrt%28+%28-60%29%5E2-4%2A1%2A500+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-60%29%2B-+sqrt%28+%28-60%29%5E2-4%2A1%2A500+%29%29%2F%282%2A1%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+=+%2860%2B-+sqrt%28+3600-2000+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860%2B-+sqrt%28+3600-2000+%29%29%2F2+\"   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+=+%2860%2B-+sqrt%28+1600+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860%2B-+sqrt%28+1600+%29%29%2F2+\"   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+=+%2860%2B-+40%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860%2B-+40%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860%2B+40%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860%2B+40%29%2F2+\"   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+=+50+ ALIGN=MIDDLE  ALT=\"x+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860-+40%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860-+40%29%2F2+\"   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+=+10+ ALIGN=MIDDLE  ALT=\"x+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=50%29 ALIGN=MIDDLE  ALT=\"highlight%28x=50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the company is producing at least <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables to have the break-even point ; so, disregard <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10+ ALIGN=MIDDLE  ALT=\"x+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. If the company sells <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables, then what is the profit? \r<BR>\n" );
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document.write( " The profit function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+R%28x%29+-+C%28x%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+R%28x%29+-+C%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29 ALIGN=MIDDLE  ALT=\"P%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2845%29 ALIGN=MIDDLE  ALT=\"P%2845%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=P%28x%29+=+180x+-3x%5E2+%2B+1500 ALIGN=MIDDLE  ALT=\"P%28x%29+=+180x+-3x%5E2+%2B+1500\"   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%2845%29+=+180%2A45+-3%2A45%5E2+%2B+1500 ALIGN=MIDDLE  ALT=\"P%2845%29+=+180%2A45+-3%2A45%5E2+%2B+1500\"   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%2845%29+=+8100+-6075+%2B+1500 ALIGN=MIDDLE  ALT=\"P%2845%29+=+8100+-6075+%2B+1500\"   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%2845%29+=+3525 ALIGN=MIDDLE  ALT=\"P%2845%29+=+3525\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> the profit the company earns if sells <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables\r<BR>\n" );
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document.write( "3. \r<BR>\n" );
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document.write( "How many tables must the company produce in order to get a profit of $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1125 ALIGN=MIDDLE  ALT=\"1125\"   DISABLED_style= \"max-width:90%; height:auto;\" >? \r<BR>\n" );
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document.write( "Set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+1125 ALIGN=MIDDLE  ALT=\"P%28x%29+=+1125\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then solve the resulting quadratic equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1125+=+180x+-3x%5E2+%2B+1500 ALIGN=MIDDLE  ALT=\"1125+=+180x+-3x%5E2+%2B+1500\"   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=3x%5E2-180x%2B1125-1500=0 ALIGN=MIDDLE  ALT=\"3x%5E2-180x%2B1125-1500=0\"   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=3x%5E2-180x-375=0 ALIGN=MIDDLE  ALT=\"3x%5E2-180x-375=0\"   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%5E2-60x-125=0 ALIGN=MIDDLE  ALT=\"x%5E2-60x-125=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >........use quadratic formula\r<BR>\n" );
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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;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-60%29+%2B-+sqrt%28+%28-60%29%5E2-4%2A1%2A%28-125%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-60%29+%2B-+sqrt%28+%28-60%29%5E2-4%2A1%2A%28-125%29+%29%29%2F%282%2A1%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+=+%2860+%2B-+sqrt%28+3600%2B500+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+sqrt%28+3600%2B500+%29%29%2F2+\"   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+=+%2860+%2B-+sqrt%28+4100+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+sqrt%28+4100+%29%29%2F2+\"   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+=+%2860+%2B-+64.03124237432849%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+64.03124237432849%29%2F2+\"   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+=+%2860+%2B-+64.03%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+64.03%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we need only positive value since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents an order\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+%2B+64.03%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B+64.03%29%2F2+\"   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+=+124.03%2F2+ ALIGN=MIDDLE  ALT=\"x+=+124.03%2F2+\"   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+=+62.01562118716424+ ALIGN=MIDDLE  ALT=\"x+=+62.01562118716424+\"   DISABLED_style= \"max-width:90%; height:auto;\" >- exact solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+62+ ALIGN=MIDDLE  ALT=\"x+=+62+\"   DISABLED_style= \"max-width:90%; height:auto;\" >round it to whole number since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents tables\r<BR>\n" );
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document.write( "4. \r<BR>\n" );
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document.write( "What happen if the company produces <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58 ALIGN=MIDDLE  ALT=\"58\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables? \r<BR>\n" );
document.write( "\n" );
document.write( "evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2858%29 ALIGN=MIDDLE  ALT=\"P%2858%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=P%2858%29+=+180%2A58+-3%2A58%5E2+%2B+1500 ALIGN=MIDDLE  ALT=\"P%2858%29+=+180%2A58+-3%2A58%5E2+%2B+1500\"   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%2858%29+=+10440+-10092+%2B+1500 ALIGN=MIDDLE  ALT=\"P%2858%29+=+10440+-10092+%2B+1500\"   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%2858%29+=+348+%2B+1500 ALIGN=MIDDLE  ALT=\"P%2858%29+=+348+%2B+1500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2858%29+=+1848 ALIGN=MIDDLE  ALT=\"P%2858%29+=+1848\"   DISABLED_style= \"max-width:90%; height:auto;\" >  => the profit the company earns if sells <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58 ALIGN=MIDDLE  ALT=\"58\"   DISABLED_style= \"max-width:90%; height:auto;\" > tables\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );