document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028708>Question 1028708</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Diver Time Company makes digital watches for scuba divers. The company models its profits with the function P(d)=-2d^2 + 13d- 6, where d is the number of watches sold in hundreds, and P(d) is the company's profit, in tens of thousands of dollars.<BR>\n" );
document.write( "a) how many watches must the company sell in order to break even? show your work.<BR>\n" );
document.write( "b)How many watches does Diver Time need to sell to maximize profits? Explain<BR>\n" );
document.write( "c) What is the maximum profit? Explain.\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks :))) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643792 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=643792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%28d%29+=+-2d%5E2+%2B+13d+-+6+ ALIGN=MIDDLE  ALT=\"+P%28d%29+=+-2d%5E2+%2B+13d+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The break even point is where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%28d%29+=+0+ ALIGN=MIDDLE  ALT=\"+P%28d%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "or no profit<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2d%5E2+%2B+13d+-+6+=+0+ ALIGN=MIDDLE  ALT=\"+-2d%5E2+%2B+13d+-+6+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+d+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-2+ ALIGN=MIDDLE  ALT=\"+a+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+13+ ALIGN=MIDDLE  ALT=\"+b+=+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-6+ ALIGN=MIDDLE  ALT=\"+c+=+-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28-13+%2B-+sqrt%28+13%5E2+-+4%2A%28-2%29%2A%28-6%29+%29%29+%2F+%282%2A%28-2%29%29+ ALIGN=MIDDLE  ALT=\"+d+=+%28-13+%2B-+sqrt%28+13%5E2+-+4%2A%28-2%29%2A%28-6%29+%29%29+%2F+%282%2A%28-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28-13+%2B-+sqrt%28+169+-+48+%29%29+%2F%28-4+%29 ALIGN=MIDDLE  ALT=\"+d+=+%28-13+%2B-+sqrt%28+169+-+48+%29%29+%2F%28-4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28-13+%2B-+sqrt%28+121+%29%29+%2F%28-4+%29 ALIGN=MIDDLE  ALT=\"+d+=+%28-13+%2B-+sqrt%28+121+%29%29+%2F%28-4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28-13+%2B+11%29+%2F%28-4+%29 ALIGN=MIDDLE  ALT=\"+d+=+%28-13+%2B+11%29+%2F%28-4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28-2%29+%2F+%28-4%29+ ALIGN=MIDDLE  ALT=\"+d+=+%28-2%29+%2F+%28-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+.5+ ALIGN=MIDDLE  ALT=\"+d+=+.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hundreds<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28+-13+-+11+%29+%2F+%28-4%29+ ALIGN=MIDDLE  ALT=\"+d+=+%28+-13+-+11+%29+%2F+%28-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+%28-24%29+%2F+%28-4%29+ ALIGN=MIDDLE  ALT=\"+d+=+%28-24%29+%2F+%28-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+6+ ALIGN=MIDDLE  ALT=\"+d+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hundreds<BR>\n" );
document.write( "There are 2 break even points:<BR>\n" );
document.write( "50 watches sold and<BR>\n" );
document.write( "600 watches sold<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "The maximum profit is where:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+p+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+-13%2F%28+2%2A%28-2%29%29+ ALIGN=MIDDLE  ALT=\"+p+=+-13%2F%28+2%2A%28-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+%28-13%29%2F%28-4%29+ ALIGN=MIDDLE  ALT=\"+p+=+%28-13%29%2F%28-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+13%2F4+ ALIGN=MIDDLE  ALT=\"+p+=+13%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2813%2F4%29%2A100+=+325+ ALIGN=MIDDLE  ALT=\"+%2813%2F4%29%2A100+=+325+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When 325 watches are sold, the profit is maximum<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-2%2C10%2C+-10%2C+16%2C+-2x%5E2+%2B+13x+-+6+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-2%2C10%2C+-10%2C+16%2C+-2x%5E2+%2B+13x+-+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );