document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4797>Question 4797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not sure what this word problem is asking, it needs to be solved using systems of linear equations.\r<BR>\n" );
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document.write( "A manufacturer produces two modles of mountain bicycles.The times(in hours) required for assembling and painting are:       Model A    Model B<BR>\n" );
document.write( "                                    Assembling    5          4<BR>\n" );
document.write( "                                    Painting      2          3<BR>\n" );
document.write( "The maximum total weekly hours available in the assembly department and the paint department are 200 hours and 108 hours, respectivley. The profits per unit are $25 for model A and $15 for model B. How many of each type should be produced to maximize profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2326 by </B><A HREF=/tutors/aboutme.mpl?userid=Abbey><B>Abbey(339)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Abbey><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=2326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can assume that maximum profits in this case will occur when there is no unused time in either department.\r<BR>\n" );
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document.write( "The assembly department has 200 hours available<BR>\n" );
document.write( "and the paint department has 108 hours available\r<BR>\n" );
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document.write( "Let A = the number of Model A bicycles built<BR>\n" );
document.write( "Let B = the number of Model B bicycles built\r<BR>\n" );
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document.write( "Assembly time:<BR>\n" );
document.write( "5A+4B=200<BR>\n" );
document.write( "Paint time:<BR>\n" );
document.write( "2A+3B=108\r<BR>\n" );
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document.write( "We have two equations:<BR>\n" );
document.write( "5A+4B=200 = <BR>\n" );
document.write( "2A+3B=108 = \r<BR>\n" );
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document.write( "Multiply the first equation by -2 and the second by 5 to eliminate:                        \r<BR>\n" );
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document.write( "-10A+ -8B= -400<BR>\n" );
document.write( " 10A+ 15B=  540                      \r<BR>\n" );
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document.write( "Add them:<BR>\n" );
document.write( "7B=140\r<BR>\n" );
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document.write( "Divide both sides by 7<BR>\n" );
document.write( "B=20\r<BR>\n" );
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document.write( "Substitute back into the original equation:\r<BR>\n" );
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document.write( "2A+3(20)=108<BR>\n" );
document.write( "2A+60=108<BR>\n" );
document.write( "2A=48<BR>\n" );
document.write( "A=24 </SPAN>\n" );
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