document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263217>Question 263217</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Worker efficiency. In a study of worker efficiency at Wong<BR>\n" );
document.write( "Laboratories it was found that the number of components<BR>\n" );
document.write( "assembled per hour by the average worker t hours after<BR>\n" );
document.write( "starting work could be modeled by the formula<BR>\n" );
document.write( "N(t)=-3t^3 + 23t^2 +8t.<BR>\n" );
document.write( "a) Rewrite the formula by factoring the right-hand side<BR>\n" );
document.write( "completely.<BR>\n" );
document.write( "b) Use the factored version of the formula to find N(3).<BR>\n" );
document.write( "c) Use the accompanying graph to estimate the time at<BR>\n" );
document.write( "which the workers are most efficient.<BR>\n" );
document.write( "d) Use the accompanying graph to estimate the<BR>\n" );
document.write( "maximum number of components assembled per<BR>\n" );
document.write( "hour during an 8-hour shift.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194069 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Laboratories it was found that the number of components<BR>\n" );
document.write( "assembled per hour by the average worker t hours after<BR>\n" );
document.write( "starting work could be modeled by the formula<BR>\n" );
document.write( "N(t)=-3t^3 + 23t^2 +8t.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) Rewrite the formula by factoring the right-hand side<BR>\n" );
document.write( "completely.<BR>\n" );
document.write( "n(t) = -3t^3 + 23t^2 + 8t <BR>\n" );
document.write( "factor out -t, changing signs makes it easier to factor<BR>\n" );
document.write( "n(t) = -t(3t^2 - 23t - 8) <BR>\n" );
document.write( "n(t) = -t(3t + 1)(t - 8)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) Use the factored version of the formula to find N(3).<BR>\n" );
document.write( "n(t) = -t(3t + 1)(t - 8)<BR>\n" );
document.write( "n(3) = -3(3(3) + 1)(3 - 8)<BR>\n" );
document.write( "n(3) = -3(10)(-5)<BR>\n" );
document.write( "n(3) = +150 units<BR>\n" );
document.write( ":<BR>\n" );
document.write( "c) Use the accompanying graph to estimate the time at<BR>\n" );
document.write( "which the workers are most efficient.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+10%2C+-50%2C+320%2C+-3x%5E3%2B23x%5E2%2B8x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+10%2C+-50%2C+320%2C+-3x%5E3%2B23x%5E2%2B8x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looks to be about 5.25 hrs, wouldn't you think?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "d) Use the accompanying graph to estimate the<BR>\n" );
document.write( "maximum number of components assembled per<BR>\n" );
document.write( "hour during an 8-hour shift. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "at 5.25 hrs it looks like 250 units per hr, however we can calculate that<BR>\n" );
document.write( "n(t) = -t(3t + 1)(t - 8)<BR>\n" );
document.write( "n(5.25) = -5.25(3(5.25) + 1)(5.25-8)<BR>\n" );
document.write( "n(5.25) = -5.25(16.75)(-2.75)<BR>\n" );
document.write( "n(5.25) = 241.8 ~ 240 units/hr would be closer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );