document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178699>Question 1178699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> this time, our immune system is the best defense . With this, a Melegail wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food A contains 2 units /kg of Vitamin A and 1 unit of /kg of vitamin C. Food B contains 1 unit/kg of vitamin A and 2 units/kg of Vitamin C. It costs 50.00 per kg to purchase food A and 70.00 per kg to purchase Food B. Formulate this problem as a linear programming problem to minimize the cost of such a mixture. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850309 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's formulate this as a linear programming problem.\r<BR>\n" );
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document.write( "**1. Define the Decision Variables:**\r<BR>\n" );
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document.write( "* Let `x` represent the number of kilograms of Food A.<BR>\n" );
document.write( "* Let `y` represent the number of kilograms of Food B.\r<BR>\n" );
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document.write( "**2. Define the Objective Function:**\r<BR>\n" );
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document.write( "* The objective is to minimize the cost.<BR>\n" );
document.write( "* Cost = 50x + 70y<BR>\n" );
document.write( "* Minimize Z = 50x + 70y\r<BR>\n" );
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document.write( "**3. Define the Constraints:**\r<BR>\n" );
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document.write( "* **Vitamin A Constraint:** The mixture must contain at least 8 units of Vitamin A.<BR>\n" );
document.write( "    * 2x + y ≥ 8<BR>\n" );
document.write( "* **Vitamin C Constraint:** The mixture must contain at least 10 units of Vitamin C.<BR>\n" );
document.write( "    * x + 2y ≥ 10<BR>\n" );
document.write( "* **Non-negativity Constraints:** The amount of food cannot be negative.<BR>\n" );
document.write( "    * x ≥ 0<BR>\n" );
document.write( "    * y ≥ 0\r<BR>\n" );
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document.write( "**Complete Linear Programming Problem:**\r<BR>\n" );
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document.write( "**Minimize:** Z = 50x + 70y\r<BR>\n" );
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document.write( "**Subject to:**\r<BR>\n" );
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document.write( "* 2x + y ≥ 8<BR>\n" );
document.write( "* x + 2y ≥ 10<BR>\n" );
document.write( "* x ≥ 0<BR>\n" );
document.write( "* y ≥ 0<BR>\n" );
document.write( " </SPAN>\n" );
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