document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23274>Question 23274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maximum cost using the quadratic equations, functions, inequalities and their graphs.  It costs Acme Manufacturing C dollars per hour to operate its golf ball division.  An analyst has determined that C is related to the number of golf balls produced per hour, x, by the equation C = 0.009x^2 - 1.8x + 100.  What number of balls per hour should Acme produce to minimize the cost per hour of manufacturing these golf balls? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12017 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=12017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Minimise:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.009x%5E2+-+1.8x+%2B+100 ALIGN=MIDDLE  ALT=\"C+=+.009x%5E2+-+1.8x+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is the equation of a parabola that opens upwards (Coefficient of x^2 is positive), so the minimum value of C would be at the parabola's vertex.  The x-coordintate of the vertex is given by: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Your equation is already in standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"C+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > so here: a = .009 and b = -1.8.  The minimum value of C will be found at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28-1.8%29%2F2%28.009%29 ALIGN=MIDDLE  ALT=\"x+=+-%28-1.8%29%2F2%28.009%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.8%2F.018 ALIGN=MIDDLE  ALT=\"x+=+1.8%2F.018\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1800%2F18 ALIGN=MIDDLE  ALT=\"x+=+1800%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+100 ALIGN=MIDDLE  ALT=\"x+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Acme should produce 100 ball per hour to minimise the cost per hour.\r<BR>\n" );
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document.write( "It might be helpful to see the graph of the cost, C (vertical axis) versus x (horizontal axis) the number of balls produced:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-20%2C200%2C-10%2C120%2C.009x%5E2-1.8x%2B100%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-20%2C200%2C-10%2C120%2C.009x%5E2-1.8x%2B100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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