document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013609>Question 1013609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A toy factory produces wooden puzzles that get sold in toy stores. The cost per puzzle, C (in dollars), to produce the puzzles, p (in hundreds) on any given day is modeled by the cost function below. <BR>\n" );
document.write( " C= 0.006p (squared) - 0.036p + 0.7 <BR>\n" );
document.write( "Find the number of puzzles that the factory should make each day to minimize the cost per puzzle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629872 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=629872\">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=+C+=+.006p%5E2+-+.036p+%2B+.7+ ALIGN=MIDDLE  ALT=\"+C+=+.006p%5E2+-+.036p+%2B+.7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is plotted on the vertical axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+ ALIGN=MIDDLE  ALT=\"+p+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is plotted on the horizontal axis<BR>\n" );
document.write( "You need to find the point ( C,p ) where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a minimum<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "The formula for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+ ALIGN=MIDDLE  ALT=\"+p+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <BR>\n" );
document.write( "minimum is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5Bmin%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+p%5Bmin%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the equation <BR>\n" );
document.write( "is in the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+a%2Ap%5E2+%2B+b%2Ap+%2B+c+ ALIGN=MIDDLE  ALT=\"+C+=+a%2Ap%5E2+%2B+b%2Ap+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+.006+ ALIGN=MIDDLE  ALT=\"+a+=+.006+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-.036+ ALIGN=MIDDLE  ALT=\"+b+=+-.036+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5Bmin%5D+=+-%28+-.036+%29+%2F+%28+2%2A.006+%29+ ALIGN=MIDDLE  ALT=\"+p%5Bmin%5D+=+-%28+-.036+%29+%2F+%28+2%2A.006+%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%5Bmin%5D+=+.036+%2F+.012+ ALIGN=MIDDLE  ALT=\"+p%5Bmin%5D+=+.036+%2F+.012+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%5Bmin%5D+=+3+ ALIGN=MIDDLE  ALT=\"+p%5Bmin%5D+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "making 3 puzzles/day will minimize<BR>\n" );
document.write( "the cost/puzzle<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+400%2C+400%2C+-20%2C+60%2C+-10%2C+50%2C+.006x%5E2+-+.036x+%2B+.7+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-20%2C+60%2C+-10%2C+50%2C+.006x%5E2+-+.036x+%2B+.7+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Answer could be right.<BR>\n" );
document.write( "Plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+3.1+ ALIGN=MIDDLE  ALT=\"+p+=+3.1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+2.9+ ALIGN=MIDDLE  ALT=\"+p+=+2.9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the<BR>\n" );
document.write( "equation and see if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a minimum in each case </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );