document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138710>Question 138710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"A company calculates it's profit by finding the difference between<BR>\n" );
document.write( "revenue and cost. The cost function of producing x hammers is C(x) =<BR>\n" );
document.write( "4x+170. If each hammer is sold for $10, the revenue function for<BR>\n" );
document.write( "selling x hammers is R (x) = 10x.\"<BR>\n" );
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document.write( "1.) How many hammers must be sold to make a profit?<BR>\n" );
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document.write( "2.) How many hammers must be sold to make a profit of $100?<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 #101212 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=101212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)\r<BR>\n" );
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document.write( "The profit function is defined by:\r<BR>\n" );
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document.write( "Profit = Revenue - Cost\r<BR>\n" );
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document.write( "So in function notation it looks like:\r<BR>\n" );
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document.write( "<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( "So in our case:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=10x-%284x%2B170%29 ALIGN=MIDDLE  ALT=\"P%28x%29=10x-%284x%2B170%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=10x ALIGN=MIDDLE  ALT=\"R%28x%29=10x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=4x%2B170 ALIGN=MIDDLE  ALT=\"C%28x%29=4x%2B170\"   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=10x-4x-170 ALIGN=MIDDLE  ALT=\"P%28x%29=10x-4x-170\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the negative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=6x-170 ALIGN=MIDDLE  ALT=\"P%28x%29=6x-170\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-170%3E0 ALIGN=MIDDLE  ALT=\"6x-170%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the right side greater than zero. Remember we're looking for positive profit.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%3E170 ALIGN=MIDDLE  ALT=\"6x%3E170\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 170 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E170%2F6 ALIGN=MIDDLE  ALT=\"x%3E170%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E28.333 ALIGN=MIDDLE  ALT=\"x%3E28.333\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E29 ALIGN=MIDDLE  ALT=\"x%3E29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Round to the nearest whole number. A third of a hammer can't be sold.\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E29 ALIGN=MIDDLE  ALT=\"x%3E29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we'll have positive profit. So more than 29 hammers must be sold to gain a profit.\r<BR>\n" );
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document.write( "<hr>\r<BR>\n" );
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document.write( "2)\r<BR>\n" );
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document.write( "We're still using the profit function. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=6x-170 ALIGN=MIDDLE  ALT=\"P%28x%29=6x-170\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we want a profit of $100, simply plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=100 ALIGN=MIDDLE  ALT=\"P%28x%29=100\"   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=6x-170 ALIGN=MIDDLE  ALT=\"P%28x%29=6x-170\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the profit function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=6x-170 ALIGN=MIDDLE  ALT=\"100=6x-170\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=100 ALIGN=MIDDLE  ALT=\"P%28x%29=100\"   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=270=6x ALIGN=MIDDLE  ALT=\"270=6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 170 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45=x ALIGN=MIDDLE  ALT=\"45=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 6\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=45 ALIGN=MIDDLE  ALT=\"x=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we'll have a profit of $100. So 45 must be sold to make a profit of $100. </SPAN>\n" );
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