document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139948>Question 1139948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A chain saw requires 3 hours of assembly and a wood chipper 5 hours. A maximum of 45 hours of assembly time is available. The profit is $ 160 on a chain saw and $ 240 on a chipper. How many of each should be assembled for maximum​ profit?<BR>\n" );
document.write( "To attain the maximum​ profit, assemble <BR>\n" );
document.write( "nothing chain saws and <BR>\n" );
document.write( "nothing wood chippers.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760459 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=760459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i solved this graphically as shown below:\r<BR>\n" );
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document.write( "the area of the graph that is not shaded is the region of feasibility.\r<BR>\n" );
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document.write( "to find that region, i graphed the opposite of the inequalities formed by the constraints of the problem.\r<BR>\n" );
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document.write( "the constraints of the problem were:\r<BR>\n" );
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document.write( "3x + 5y <= 45<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "i graphed:\r<BR>\n" );
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document.write( "3x + 5y >= 45<BR>\n" );
document.write( "x <= 0<BR>\n" );
document.write( "y <= 0\r<BR>\n" );
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document.write( "the corner points of the feasible region are where the maximum / minimum solutions lie.\r<BR>\n" );
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document.write( "the objective function, which was profit = 160x + 240y, was evaluated at each of these corner points.\r<BR>\n" );
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document.write( "at (0,9), the profit was 240 * 9 = 2160\r<BR>\n" );
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document.write( "at (15,0), the profit was 160 * 15 = 2400.\r<BR>\n" );
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document.write( "maximum profit was 2400 when 15 chains saws and zero chippers were assembled.\r<BR>\n" );
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document.write( "unfortunately, there was no happy middle ground for maximum profit.\r<BR>\n" );
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document.write( "for example, when x = 5, y = 6 and the profit was 160 * 5 + 240 * 6 = 2240.\r<BR>\n" );
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document.write( "that was actually better than one of the corner points but not better than the other.\r<BR>\n" );
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