document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054323>Question 1054323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Queuing Theory <BR>\n" );
document.write( "Suppose customers arrive at a fast-food service window at a rate of 9 people per hour. With reasonable assumptions, the average time(in hours) that a customer will wait in line before being served is modeled by f(x)=9/x(x-9) where x is the average # of people being served per hour.<BR>\n" );
document.write( "A)Why is the function meaningless if the average # of people served per hour is less then 9?\r<BR>\n" );
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document.write( "Suppose the average time to serve a customer is 5 minutes.<BR>\n" );
document.write( "B)How many customers can be served in an hour?<BR>\n" );
document.write( "C)How many minutes will a customer have to wait in line (on the average)?<BR>\n" );
document.write( "D)Suppose we want to halve the average waiting time to 7.5 minutes (1/8 hour). How fast must an employee work to serve a customer (on the average)?(convert to minutes)How might this reduction in serving time be accomplished?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #669651 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=669651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) the function is negative for the average # of people served per hour is less than 9<BR>\n" );
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document.write( "B) 60 / 5 = 12 people served per hour<BR>\n" );
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document.write( "C) f(12) = 9 / (12(12-9)) = 9/36 = 1/4 = 15 minutes<BR>\n" );
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document.write( "D) 1/8 = 9 / (x(x-9))<BR>\n" );
document.write( "x^2 -9x = 72<BR>\n" );
document.write( "x^2 -9x -72 = 0<BR>\n" );
document.write( "Use quadratic formula to solve for x<BR>\n" );
document.write( "x = (9 + 19.20) / 2 = 14.10<BR>\n" );
document.write( "x = (9 - 19.20) / 2 = -5.10<BR>\n" );
document.write( "we want the positive value 14.10 approx 14 people<BR>\n" );
document.write( "60 / 14 = 4.2857 minutes service time<BR>\n" );
document.write( "Add another employee and another service window<BR>\n" );
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