document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205327>Question 1205327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An individual needs a daily supplement of at least 510 units of vitamin C and 266 of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 102 units of vitamin C and 19 units of vitamin E, while each ounce of food II contains 51 units of vitamin C and also 38 units of vitamin E. The total supplement of these two foods must be at most 21 ounces. Unfortunately, food I contains 19 units of cholesterol per ounce and food II contains 13 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. Find the minimum amount of cholesterol.\r<BR>\n" );
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document.write( "amount of food I<BR>\n" );
document.write( "amount of food II	 	<BR>\n" );
document.write( "minimum cholesterol	 	\r<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 #842054 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=842054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "An individual needs a daily supplement of at least 510 units of vitamin C and 266 of vitamin E <BR>\n" );
document.write( "and agrees to obtain this supplement by eating two foods, I and II. <BR>\n" );
document.write( "Each ounce of food I contains 102 units of vitamin C and 19 units of vitamin E, while <BR>\n" );
document.write( "each ounce of food II contains 51 units of vitamin C and also 38 units of vitamin E. <BR>\n" );
document.write( "The total supplement of these two foods must be at most 21 ounces. <BR>\n" );
document.write( "Unfortunately, food I contains 19 units of cholesterol per ounce and food II contains 13 units of cholesterol per ounce. <BR>\n" );
document.write( "Find the appropriate amounts of the two food supplements so that cholesterol is minimized. Find the minimum amount of cholesterol.\r<BR>\n" );
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document.write( "amount of food I<BR>\n" );
document.write( "amount of food II	 	<BR>\n" );
document.write( "minimum cholesterol	 	<BR>\n" );
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document.write( "The solution by @Theo is incorrect.\r<BR>\n" );
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document.write( "It is incorrect, because Theo incorrectly treats the condition <BR>\n" );
document.write( "\"The total supplement of these two foods must be at most 21 ounces.\"\r<BR>\n" );
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document.write( "Theo writes for it \r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x + y >= 21 \r<BR>\n" );
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document.write( "in his basic restrictions,  &nbsp;while the correct treatment is \r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x + y  <= 21  &nbsp;&nbsp;&nbsp;&nbsp;(\"at most\").\r<BR>\n" );
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document.write( "The solution by @math_tutor2020 is correct.\r<BR>\n" );
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document.write( "The only essential note to the @math_tutor2020 solution is that the dashed lines<BR>\n" );
document.write( "in his plot DO BELONG to the solution region.\r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );