document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044895>Question 1044895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: It costs $0.30 for Tina to produce a glass of lemonade. If she charges p dollars for one glass, she believes she can sell 50 - p glasses of lemonade in a day. Find a quadratic function that gives Tina's daily profit as a function of price. Then graph Tina's profit as a function of price.\r<BR>\n" );
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document.write( "Answer: This is as far as I got - any help appreciated.\r<BR>\n" );
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document.write( "I thought if X = glasses sold then X = (50-p). And Profit would be the price of one glass (p) - 0.30, then Total Profit would be = (50-p)(p-0.30). I then tried to use algebra to simplify this, and think I came unstuck. I used the FOIL method (first, outer, inner, last). So F (50 * p) = 50P. O (50*-0.30) = - 15. I (-p * p) = -p^2. L (-p*-0.30) = 3P/10. So the final equation would be -p^2 + 50p - 3P/10 - 15. I then got lost as to how to simplify 50p - 3p/10. Thanks 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 #660321 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=660321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> DAILY PROFIT is (number of glasses)*(price)-(cost of 1 glass)*(number of glasses)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2850-p%29-%280.3%29%28p%29 ALIGN=MIDDLE  ALT=\"p%2850-p%29-%280.3%29%28p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using p for price; compare to the description and then try simplifying.\r<BR>\n" );
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document.write( "If you choose y as the profit, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=p%2850-p%29-0.3p%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=p%2850-p%29-0.3p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Remember, you chose x, which I am now choosing as the lower-case form, for number of glasses lemonade sold.  If x is number of glasses sold, and 50-p glasses expected to be sold, then 50-p=x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=50p-p%5E2-0.3p ALIGN=MIDDLE  ALT=\"y=50p-p%5E2-0.3p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-p%5E2-0.3p%2B50p ALIGN=MIDDLE  ALT=\"y=-p%5E2-0.3p%2B50p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-p%5E2%2B49.7p ALIGN=MIDDLE  ALT=\"y=-p%5E2%2B49.7p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "More easily used factored,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-p%28p%2B49.7%29 ALIGN=MIDDLE  ALT=\"y=-p%28p%2B49.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=p%2849.7-p%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y=p%2849.7-p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--------a parabola with a maximum value, which occurs  in exact middle of 0 and 49.7.  You will want the nearest whole number to this middle value of p. </SPAN>\n" );
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