document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068413>Question 1068413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this question.<BR>\n" );
document.write( "A restaurant decides to add homemade desserts to their menu. When they sell the desserts for $7 each, they sell 80 desserts in a week. When they raise the price to $9 each, they sell 40 desserts in a week.<BR>\n" );
document.write( "a.  Write a linear function f(x) that relates x desserts sold to the price f(x) of the desserts.<BR>\n" );
document.write( "b.  The desserts cost the restaurant $2 each to make. Write a profit function P(x) that gives the total profit for selling x desserts. (Hint: total profit= profit per item times number of items sold)<BR>\n" );
document.write( "c.  Use your profit function to find the number of desserts that maximizes profit, and then find the price that maximizes profit.<BR>\n" );
document.write( "Thank you in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683627 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=683627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x,y) for x number of deserts and y price of a desert\r<BR>\n" );
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document.write( "Points  (80,7) and (40,9).<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "b=y-mx<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%289-7%29%2F%2840-80%29%29x%2B%289%2B%281%2F20%2940%29 ALIGN=MIDDLE  ALT=\"y=%28%289-7%29%2F%2840-80%29%29x%2B%289%2B%281%2F20%2940%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F20%29x%2B9%2B2 ALIGN=MIDDLE  ALT=\"y=-%281%2F20%29x%2B9%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F20%29x%2B11 ALIGN=MIDDLE  ALT=\"y=-%281%2F20%29x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Calling this price function f,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=-%281%2F20%29x%2B11%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=-%281%2F20%29x%2B11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "SELL x DESERTS<BR>\n" );
document.write( "Cost <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Revenue  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Af%28x%29=x%28-%281%2F20%29x%2B11%29=-x%5E2%2F20%2B11x ALIGN=MIDDLE  ALT=\"x%2Af%28x%29=x%28-%281%2F20%29x%2B11%29=-x%5E2%2F20%2B11x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "PROFIT FUNCTION  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-x%5E2%2F20%2B11x-2x ALIGN=MIDDLE  ALT=\"P%28x%29=-x%5E2%2F20%2B11x-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or simplified,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P%28x%29=-x%5E2%2F20%2B9x%29 ALIGN=MIDDLE  ALT=\"highlight%28P%28x%29=-x%5E2%2F20%2B9x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can look for the maximum P. </SPAN>\n" );
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