document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199721>Question 199721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me with this problem:\r<BR>\n" );
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document.write( "Find the value(s) of the function, subject to the system of inequalities.<BR>\n" );
document.write( "Find the maximum and minimum of P = 10x - 16y subject to:\r<BR>\n" );
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document.write( "0 < X < 5, 0 < Y < 8, 4x + 5y < 30, and 4x + 3y < 20<BR>\n" );
document.write( "***ALL OF THE < SIGNS HAVE A LINE UNDER THEM***\r<BR>\n" );
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document.write( "a. -96, 0<BR>\n" );
document.write( "b. -67.5, -96<BR>\n" );
document.write( "c. 50, -96 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150112 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=150112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Wish I had a nice tool to do this, but I don't. In this case, I used trial and error.\r<BR>\n" );
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document.write( "Let's look at the answers first. <BR>\n" );
document.write( "a) can't be correct since a max of -96 and a min of 0 doesn't make sense.\r<BR>\n" );
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document.write( "Let's look at c) next. Those numbers look good, so let's see if we can work backwards to values for x and y. Then we can use the givne constraints to see if they are satisfied.<BR>\n" );
document.write( "First, look at P, You can see that P grows as x gets larger and shrinks as y get larger. So, pick the largest value allowed for x and the the smallest one allowed for y. That means pick x=5 and y =0. If we use (5,0), then P=50. So far, so good. Now check the other constraints. Is 4x + 5y <= 30, and 4x + 3y <= 20 satisfied at (5,0)? Yes. So (5,0) still looks OK.<BR>\n" );
document.write( "What about a minimum?<BR>\n" );
document.write( "In that case, use the smallest x and the largest y. So (0,8) yields the minimum for P. Test the contraints  4x + 5y <= 30, and 4x + 3y <= 20 satisfied at (0,8)? No. So let's pin x at 0 and see what value for y works for the constraints. You can see the first one says y<=6 and the second says y<=20/3. So y=6 fits for both. Try point (0,6). What is P then? P = 10*0 - 16*6 = -96\r<BR>\n" );
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document.write( "c) is the answer\r<BR>\n" );
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document.write( "the values in b) are valid, but the max is incorrect </SPAN>\n" );
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