document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106877>Question 106877</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.<BR>\n" );
document.write( "CAN YOU PLEASE HELP ME WORK THIS PROBLEM OUT IN FULL PLEASE?\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 #77923 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77923\">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( ":<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( ":<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( "Assembly:<BR>\n" );
document.write( "3x + 5y =< 3900<BR>\n" );
document.write( "5y =< -3x + 3900; arrange in the \"y=\" form for graphing<BR>\n" );
document.write( "y =< -.6x + 780; divided equation by 5<BR>\n" );
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document.write( "Detail<BR>\n" );
document.write( "1x + 3y =< 2100<BR>\n" );
document.write( "3y =< -x + 2100<BR>\n" );
document.write( "y =< .33x + 700; divided equation by 3<BR>\n" );
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document.write( "QA & Packing<BR>\n" );
document.write( "2x + 2y =< 2200<BR>\n" );
document.write( "2y =< -2x + 2200<BR>\n" );
document.write( "y =< -x + 1100; divided equation by 2<BR>\n" );
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document.write( "Graph this and you should have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-100%2C+1500%2C+-100%2C+1000%2C+-.6x%2B780%2C+-.33x%2B700%2C+-x%2B1100%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that the area of feasibility is at or below the the lowest graphing line<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( "Find the coordinates of the corners of the area of feasibility, use these to<BR>\n" );
document.write( "make an objective profit function for each corner.<BR>\n" );
document.write( "The x/y values of the corners will be:<BR>\n" );
document.write( "0, 700<BR>\n" );
document.write( "300, 600<BR>\n" );
document.write( "800, 300<BR>\n" );
document.write( "1100, 0<BR>\n" );
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document.write( "0,700: <BR>\n" );
document.write( "100x + 150y =<BR>\n" );
document.write( "100(0) + 150(700) = $105,000 profit<BR>\n" );
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document.write( "300,600<BR>\n" );
document.write( "100(300) + 150(600) =<BR>\n" );
document.write( "30000 + 90000 = $120,000 profit<BR>\n" );
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document.write( "800,300<BR>\n" );
document.write( "100(800) + 150(300) = <BR>\n" );
document.write( "80000 + 45000 = $125,000 profit<BR>\n" );
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document.write( "1100, 0 <BR>\n" );
document.write( "100(1100) + 150(0) = $110,000 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" );
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document.write( "I am pressed for time, here. Substitute 170 for 150 and do the same as<BR>\n" );
document.write( "above. If you have any questions email me, I will respond tonight.\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.  </SPAN>\n" );
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