document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131909>Question 1131909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The head of a management information center wants to staff consulting stations with two shifting teams. Team A will comprise of 3 senior programmers and 3 system analysts and Team B will consists of 2 senior programmers and 5 system analysts.<BR>\n" );
document.write( "The director wants to use no more than 42 individuals. There will be at least 48 hours to be filled during the week, with Team A shift serving for 4 hours and Team B shift serving 3 hours. The cost of Team A per shift is 3200$ per hour and 2800$ per hour for a Team B per shift. <BR>\n" );
document.write( "Determine the number of shifts of each team in order to minimize the cost. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748903 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "When I first read this problem a few days ago, the wording seemed confusing, so I didn't spend any time looking at it.  Now several days have passed, and nobody has provided a response; so I thought I would take the time to try to decipher the problem.<br><BR>\n" );
document.write( "Unfortunately, that time was wasted, because I could not find any sensible interpretation of the problem.<br><BR>\n" );
document.write( "But since I spent the time, I thought I would give you my feedback so you can see if you have not stated the problem correctly.<br><BR>\n" );
document.write( "Shifts are staffed by either team A or team B.<BR>\n" );
document.write( "team A has 3 senior programmers and 3 system analysts; team B has 2 senior programmers and 5 system analysts.<BR>\n" );
document.write( "team A shifts are 4 hours; team B shifts are 3 hours.<BR>\n" );
document.write( "The objective is to minimize the cost of a minimum of 48 hours of work at a cost of $3200 per hour for team A and $2800 per hour for team B; that is $12,800 per shift for team A shifts and $8400 per shift for team B shifts.<br><BR>\n" );
document.write( "Let A be the number of shifts for team A<BR>\n" );
document.write( "Let B be the number of shifts for team B<br><BR>\n" );
document.write( "Then the requirement of filling 48 hours of shifts gives us the following constraint:<br><BR>\n" );
document.write( "(1) 4A + 3B >= 48<br><BR>\n" );
document.write( "That's as far as I can get making any sense out of the problem.<br><BR>\n" );
document.write( "The other given information is that the director \"wants to use no more than 42 individuals\".  I can't see how to use that; I see two possible interpretations, neither of which leads to a solvable problem.<br><BR>\n" );
document.write( "One possibility is that every team A shift is staffed by the same people, and every team B shift is staffed by the same people.  In that case, the total number of people used is only 13; so the requirement to use no more than 42 individuals is satisfied.  But that leaves us with only one constraint; and the problem can't be solved with only one constraint.<br><BR>\n" );
document.write( "The other possibility is that every team A shift uses a different 6 people and every team B shift uses a different 7 people.  That would lead to the following constraint:<br><BR>\n" );
document.write( "(2) 6A + 7B <= 42<br><BR>\n" );
document.write( "But there are no solutions in positive integers for constraints (1) and (2) -- so again the problem can't be solved.<br>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );