document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131750>Question 1131750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company invests in a project and it has been estimated that after x months of running, the cumulative profit (€000) for the project is given by the function -3x(squared) + 31.5x - 60, where x represents time in months. The project can run for nine months at the most. \r<BR>\n" );
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document.write( "I. Draw a graph which represents the profit function <BR>\n" );
document.write( "2. Calculate the breakeven point<BR>\n" );
document.write( "3. What is the initial cost of the project?<BR>\n" );
document.write( "4. Use the graph to estimate the best time to end the project.<BR>\n" );
document.write( "5. Etimate the profit or loss at 1.5months<BR>\n" );
document.write( "6. Estimate the months where there will be a profit of €10,000 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748622 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748622\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Profit (in thousands) after x months: P(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2%2B31.5x-60 ALIGN=MIDDLE  ALT=\"-3x%5E2%2B31.5x-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph, showing the profit function (red) and (for part 6) where the profit is 10000 (green)...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C12%2C-10%2C30%2C-3x%5E2%2B31.5x-60%2C10%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C12%2C-10%2C30%2C-3x%5E2%2B31.5x-60%2C10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use your graphing calculator....!<br><BR>\n" );
document.write( "(1) graph the function (a good window is -10 to 10 by -10 to 30)<BR>\n" );
document.write( "(2) breakeven point(s) -- where the profit function is 0; estimate or use your graphing calculator<BR>\n" );
document.write( "(3) initial --> x=0; evaluate the function at x=0.  Since the revenue is initially 0, the initial cost is -P(0). (You could use your graphing calculator to evaluate P(0); but it's easier just to evaluate P(0) by looking at the function)<BR>\n" );
document.write( "(4) best time to end: when the profit is maximum (find vertex of the parabola using your calculator)<BR>\n" );
document.write( "(5) profit at 1.5. months: estimate, or evaluate P(1.5) using your calculator<BR>\n" );
document.write( "(6) graph P(x)=10 (green line on graph) along with the profit function and find where they intersect (estimate or use your graphing calculator)  </SPAN>\n" );
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