document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284169>Question 284169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company's profit, in thousands of dollars, on sales of computers is modelled by the function P(x)= -2(x-3)^2+ 50, where x is in thousands of dollars, on sales of computers sold. The company's profit, in thousands of dollars, on sales of stereo systems is modelled by the function P(x) = -(x-2)(x-7), where x is in thousands of stereo sytems sold. Calculate the maximum profit the business can earn. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206191 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=206191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A company's profit, in thousands of dollars, on sales of computers is modeled by the function P(x)= -2(x-3)^2+ 50, where x is in thousands of dollars, on sales of computers sold. The company's profit, in thousands of dollars, on sales of stereo systems is modeled by the function P(x) = -(x-2)(x-7), where x is in thousands of stereo sytems sold. Calculate the maximum profit the business can earn.<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Max profit on sales of computers: Vertex is (3,50) so max = $50K<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Max profit on sales of stereos:<BR>\n" );
document.write( "P(x) = -[x^2-9x+14]<BR>\n" );
document.write( "P(x) = -x^2+9x-14<BR>\n" );
document.write( "a = -1 ; b = -9 <BR>\n" );
document.write( "Max occurs at x = -b/2a = -9/(-2) = 4.5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Profit when x = 4.5 <BR>\n" );
document.write( "P(4.5) = -(4.5-2)(4.5-7)<BR>\n" );
document.write( "P(4.5) = -(2.5)(-2.5) = $6.25K<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "Total Max Profit: 50K + 6.25K = $56.25K<BR>\n" );
document.write( "==========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );