document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85263>Question 85263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The minimum value of z = 4x + 10y subject to\r<BR>\n" );
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document.write( "3x + y (is less or equal to) 24<BR>\n" );
document.write( "6x + 4y (is less or equal to) 66<BR>\n" );
document.write( "x (is more or equal to) 0,  y (is more or equal to) 0\r<BR>\n" );
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document.write( "is\r<BR>\n" );
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document.write( "A. 165<BR>\n" );
document.write( "B. 110<BR>\n" );
document.write( "C. 44<BR>\n" );
document.write( "D. 32 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61634 by </B><A HREF=/tutors/aboutme.mpl?userid=scianci><B>scianci(186)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scianci><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=61634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You need to test the extreme or \"corner\" points. These are (8 , 0) [8 is the biggest value x can be according to the first constraint, which in turn would make y = 0] , (0 , 24) [24 is the biggest value y can be according to the first constraint, which in turn would make x = 0] , (11 , 0) [11 is the biggest value x can be according to the second constraint, which in turn would make y = 0] , (0 , 16.5) [16.5 is the biggest value y can be according to the second constraint, which in turn would make x = 0]. Now, (0 , 24) doesn't conform to the second constraint and (11 , 0) doesn't conform to the first constraint, so they can be ruled out. So you need to plug in (8 , 0) and (0 , 16.5) into the expression 4x + 10y to get the respective values for z in each case:\r<BR>\n" );
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document.write( "4(11) + 10(0) = 44<BR>\n" );
document.write( "4(0) + 10(16.5) = 165<BR>\n" );
document.write( "44 is the smallest, so the answer is C. </SPAN>\n" );
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