document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=542467>Question 542467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A printing press has 8 machines, each of which has a speed of 3 600 prints per hour. It costs P50 to set up each machine for a run and (100+60 n ) pesos to run n machines for 1 hour. How many printing press machines should be used to produce 50 000 copies of calendars most profitably? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354589 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> most profitably sounds like least cost, since we don't know the revenue.<BR>\n" );
document.write( "the equation will be:<BR>\n" );
document.write( "cost = 50*n + (100+60n)*h<BR>\n" );
document.write( "n is the number of machines.<BR>\n" );
document.write( "h is the number of hours.<BR>\n" );
document.write( "this assumes that 50 dollars is setup costs for each machine regardless how long it runs.<BR>\n" );
document.write( "this also assumes that 100 is fixed for any number of machines to be run for 1 hour and 60 is variable cost per machine to be run for 1 hour.<BR>\n" );
document.write( "an example would be:<BR>\n" );
document.write( "cost for 2 machines run for 2 hours would be:\r<BR>\n" );
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document.write( "50 pesos * 2 machines = 100 pesos setup cost regardless of the number of hours run by each machine.<BR>\n" );
document.write( "this  is the cost per machine.\r<BR>\n" );
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document.write( "2 hours * 100 pesos = 200 pesos run cost for 2 hours regardless of the number of machines.<BR>\n" );
document.write( "this is the cost per run per hour.\r<BR>\n" );
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document.write( "2 hours * 60 pesos * 2 machines = 240 pesos run cost for 2 hours of 2 machines.<BR>\n" );
document.write( "this is the cost per machine per run per hour.\r<BR>\n" );
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document.write( "total cost for the 2 machines to be run for 2 hours would then be 100 + 200 + 240 = 450 pesos.\r<BR>\n" );
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document.write( "i used excel to analyze each scenario and came up with a minimum cost solution at 5 machines.\r<BR>\n" );
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document.write( "5 machines would take 50,000 / (3600*5) = 2.78 hours to run.\r<BR>\n" );
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document.write( "the cost for 5 machines would be:\r<BR>\n" );
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document.write( "5*50 = 250 total set up cost.<BR>\n" );
document.write( "2.78 * 100 = 278 total run cost per hour<BR>\n" );
document.write( "2.78 * 5 * 60 = 834 total run cost per machine per hour<BR>\n" );
document.write( "grand total = 250 + 278 + 834 = 1362\r<BR>\n" );
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document.write( "i was able to generate an eqaution for graphing purposes.<BR>\n" );
document.write( "that equation is:\r<BR>\n" );
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document.write( "y = (1800x^2 + 30000x + 50000)/(36x)\r<BR>\n" );
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document.write( "the graph of that equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-15%2C15%2C-3000%2C3000%2C%281800x%5E2%2B30000x%2B50000%29%2F%2836x%29%2C1362%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "just draw a vertical line at x = 5 and you will see that it intersects the graph of the equation when y = 1362.\r<BR>\n" );
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document.write( "the results from excel indicated the following:\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "number of machines\r\n" );
document.write( "      number of hours		\r\n" );
document.write( "                 total cost per machine\r\n" );
document.write( "                          total cost per hour\r\n" );
document.write( "                                        total cost per machine per hour\r\n" );
document.write( "                                                     grand total\r\n" );
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document.write( "1     13.89      50       1388.89       833.33       2272.22	\r\n" );
document.write( "2     6.94       100      694.44        833.33       1627.78	\r\n" );
document.write( "3     4.63       150      462.96        833.33       1446.30	\r\n" );
document.write( "4     3.47       200      347.22        833.33       1380.56	\r\n" );
document.write( "5     2.78       250      277.78        833.33       1361.11	*****\r\n" );
document.write( "6     2.31       300      231.48        833.33       1364.81	\r\n" );
document.write( "7     1.98       350      198.41        833.33       1381.75	\r\n" );
document.write( "8     1.74       400      173.61        833.33       1406.94\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "note that total cost per machine per hour is the same.<BR>\n" );
document.write( "this effectively cancels it out as a criteria for least cost.<BR>\n" );
document.write( "the reason for this is because the number of hours times the number of machines works out to be the same.\r<BR>\n" );
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document.write( "1 machine takes 50,000 / 3600 = 13.89 hours<BR>\n" );
document.write( "8 machines take 50,000 / (3600*8) = 1.74 hours each for a total of 13.89 hours.<BR>\n" );
document.write( "the total number of machine hours is the same, but the total number of hours spent is different because they are working in parallel to each other.<BR>\n" );
document.write( "	\r<BR>\n" );
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document.write( " </SPAN>\n" );
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