document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201272>Question 1201272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've tried and am completely lost on this.. Any help would be highly appreciated! A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $1.00, and each Type B souvenir will result in a profit of $1.40. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 3 hours available on Machine I and 5 hours available on Machine II.<BR>\n" );
document.write( "(a) For a meaningful solution, the time available on Machine II must lie between <BR>\n" );
document.write( " and min. (Enter your answers from smallest to largest.)\r<BR>\n" );
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document.write( "(b) If the time available on Machine II is changed from 300 min to (300 + k)<BR>\n" );
document.write( " min, with no change in the maximum capacity for Machine I, then Ace Novelty's profit is maximized by producing <BR>\n" );
document.write( "  Type A souvenirs and <BR>\n" );
document.write( "  Type B souvenirs, where<BR>\n" );
document.write( "? ≤ k ≤? \r<BR>\n" );
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document.write( "(c) Find the shadow price for Resource 2 (associated with constraint 2). (Round your answer to the nearest cent.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836086 by </B><A HREF=/tutors/aboutme.mpl?userid=carrollmary87><B>carrollmary87(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=carrollmary87><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=836086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can do A and B, so I hope that helps.  <BR>\n" );
document.write( "First, A is a system of equations for the two machines.  Also known as linear programming.  The machine I is 2A + 1B = 180 min.  and Machine II is 1A + 3B = 300, so using either matrix, substitution, or elimination.  <BR>\n" );
document.write( "2(1A + 3B = 300) is 2A + 6B = 600 subtract 2A + 1B = 180<BR>\n" );
document.write( " 2A + 6B = 600<BR>\n" );
document.write( "-2A - 1B = -180<BR>\n" );
document.write( "     5B = 420<BR>\n" );
document.write( "B = 84, then substitute B into one of the equations.  1A + 3(84) = 300<BR>\n" );
document.write( "A = 48<BR>\n" );
document.write( "Profit then for the company is 1(48) + 1.4(84) = 165.60\r<BR>\n" );
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document.write( "B) is asking if you increase the minutes for the maximum profit.  Max profit would be no A and all B.  because you make more money on B.<BR>\n" );
document.write( "Since the first restraint for B is machine 1:  2(0) + B = 180, then you can only make 180 B parts because of machine 1's limits.  <BR>\n" );
document.write( "Machine 2 is 1(0) + 3B = 300 + k where 0 + 3(180) = 300 + 240 (540 min total)<BR>\n" );
document.write( "so the range for k is <BR>\n" );
document.write( "1 < = k < = 240\r<BR>\n" );
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document.write( "If I understand C correctly, the answer is 1.4 (180) = $252 </SPAN>\n" );
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