document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182966>Question 1182966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An oil refinery refines types 1 and 2 of crude oil and can refine as much as 4000 barrels each week. Type 1 crude has 2 kg of impurities per barrel, type 2 has 3 kg of impurities per barrel,and the refinery can handle no more than 9000 kg of these impurities each week.How much of each type should be refined in order to maximize profits, if the profit is R25/barrel for type 1 and R30/barrel for type 2?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813097 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=813097\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of barrels of type 1<BR>\n" );
document.write( "y = number of barrels of type 2\r<BR>\n" );
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document.write( "your constraints are:\r<BR>\n" );
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document.write( "x + y <= 4000<BR>\n" );
document.write( "2x + 3y <= 9000\r<BR>\n" );
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document.write( "your would graph the opposite of these inequalities in the desmos.com calculator.\r<BR>\n" );
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document.write( "the unshaded area is your region of feasibility.<BR>\n" );
document.write( "the maximum profit is at the corners of the region of feasibility.\r<BR>\n" );
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document.write( "your graph looks like this:\r<BR>\n" );
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document.write( "your corner points are (x,y) = (0,3000), (3000,1000), (4000,0)\r<BR>\n" );
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document.write( "your objective function is 25x + 30y.<BR>\n" );
document.write( "this is what you want to maximize.\r<BR>\n" );
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document.write( "you evalute the objective function at each of your corner points.\r<BR>\n" );
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document.write( "(0,3000) = 0 * 25 + 3000 * 30 = 90,000<BR>\n" );
document.write( "(3000,1000) = 3000 * 25 + 1000 * 30 = 105,000<BR>\n" );
document.write( "(4000,0) = 4000 * 25 + 0 * 30 = 100,000\r<BR>\n" );
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document.write( "your maximum profit is when you refine 3000 barrels of type 1 and 1000 barrels of type 2.\r<BR>\n" );
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document.write( "all your constraints need to be satisfied.\r<BR>\n" );
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document.write( "at your maximum point of (3000,1000), .....\r<BR>\n" );
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document.write( "x + y = 4000 <= 4000<BR>\n" );
document.write( "2x + 3y = 2 * 3000 + 3 * 1000 = 6000 + 3000 = 9000 <= 9000\r<BR>\n" );
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document.write( "all your constraints are satisfied at your maximum profit point.\r<BR>\n" );
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document.write( "all looks good.\r<BR>\n" );
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document.write( "your solution is that 3000 barrels of type 1 and 1000 barrels of type 2 need to be refined for maximum profit.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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