document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106606>Question 106606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is one of the hardest problems I have even seen!  Can you please see if you can help with this one?  I feel like I can write some functions, but I am really confused.\r<BR>\n" );
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document.write( "Product x:  Each item sold produces $100 profit<BR>\n" );
document.write( "Labor cost: is 3 hours for assembly, 1 hour in detail work, and 2 hours for QA & packing product.\r<BR>\n" );
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document.write( "Product y:  Each item sold produces $150 profit<BR>\n" );
document.write( "Labor cost: is 5 hours for assembly, 3 hour in detail work, and 2 hours for QA & packing product.\r<BR>\n" );
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document.write( "Company has these hours available for production for each accounting period:<BR>\n" );
document.write( "3900 hours for assembly, 2100 hours for detail work, & 2200 hours for QA & packing.\r<BR>\n" );
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document.write( "Questions are:<BR>\n" );
document.write( "1) How many products of both x & y should be produced to make a max & min profit?<BR>\n" );
document.write( "2) Now what if product y profit goes up to $170 each.  How many products are needed to make a max & min profit?\r<BR>\n" );
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document.write( "I know this is not an easy question, but do you think you could help with this question please?  Thank you kindly.  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77594 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=77594\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Product x: Each item sold produces $100 profit<BR>\n" );
document.write( "Labor cost: is 3 hours for assembly, 1 hour in detail work, and 2 hours for QA & packing product. <BR>\n" );
document.write( "Product y: Each item sold produces $150 profit<BR>\n" );
document.write( "Labor cost: is 5 hours for assembly, 3 hour in detail work, and 2 hours for QA & packing product. <BR>\n" );
document.write( "Company has these hours available for production for each accounting period:<BR>\n" );
document.write( "3900 hours for assembly, 2100 hours for detail work, & 2200 hours for QA & packing. <BR>\n" );
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document.write( "Profit function: Profit = 100x + 150y<BR>\n" );
document.write( "Assembly : 3x+5y<=3900<BR>\n" );
document.write( "Detail   : x +3y<=2100<BR>\n" );
document.write( "QA&Pack  : 2x+2y<=2200<BR>\n" );
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document.write( "Questions are:<BR>\n" );
document.write( "1) How many products of both x & y should be produced to make a max & min profit?<BR>\n" );
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document.write( "You have to develop a solution set for the Assembly/Detail/QA&Pack inequalities<BR>\n" );
document.write( "Then you have to determine the coordinates of the vertices of this solution <BR>\n" );
document.write( "set.<BR>\n" );
document.write( "Then you have to substitute the x/y values of each of these vertices into<BR>\n" );
document.write( "the Profit function to see where you get a maximum profit and where you get<BR>\n" );
document.write( "a minimum profit.<BR>\n" );
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document.write( "2) Now what if product y profit goes up to $170 each. How many products are needed to make a max & min profit? <BR>\n" );
document.write( "The only thing that will change is the Profit function; it will become<BR>\n" );
document.write( "Profit = 100x + 170y<BR>\n" );
document.write( "To find the man or min you follow the same procedure you did with the <BR>\n" );
document.write( "former Profit equation.<BR>\n" );
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document.write( "This whole procedure is called linear programming.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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