document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141899>Question 1141899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Formulate but do not solve the following exercise as a linear programming problem.\r<BR>\n" );
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document.write( "A hunger-relief organization has earmarked between $2 million and $3.5 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 million and $1.75 million (inclusive), and Country B is to receive at least $0.25 million. It has been estimated that each dollar spent in Country A will yield an effective return of $0.40, whereas a dollar spent in Country B will yield an effective return of $0.70. How should the aid be allocated if the money, in millions, is to be utilized most effectively according to these criteria?<BR>\n" );
document.write( "Hint: If x and y denote the amount of money, in millions of dollars, to be given to Country A and Country B, respectively, then the objective function to be maximized is <BR>\n" );
document.write( "P = 0.4x + 0.7y.\r<BR>\n" );
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document.write( "max amount both countries receive collectively	    	x + y	 ≤ 	 <BR>\n" );
document.write( "min amount both countries receive collectively		x + y	≥	 <BR>\n" );
document.write( "max amount Country A receives		x	≤	 <BR>\n" );
document.write( "min amount Country A receives		x	≥	 <BR>\n" );
document.write( "min amount Country B receives		y	≥	 <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 #762546 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Maximize the objective function P = 0.4x + 0.7y \r<BR>\n" );
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document.write( "under these constraints\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    x + y >= 2,000,000\r\n" );
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document.write( "    x + y <= 3,5000,000\r\n" );
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document.write( "    1,000,000 <= x <= 1,750,000\r\n" );
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document.write( "    y >= 250,000.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Answered.\r<BR>\n" );
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