document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199840>Question 1199840</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABC Dairy Company wishes to make a new cheese from two of its current cheeses: Cheese X and Cheese Y. The mixture is to weight at least than 4 pounds and is to contain 6 ounces of the sharpness Ingredients S. Each pound of X costs $4 and contains 3 ounces of S, whereas each pound of Y costs $1 and contains one ounce of S. find the minimum cost of the mixture if the amount of Cheese Y cannot exceed the amount of Cheese X by more than one pound. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848451 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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=848451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Define Variables**\r<BR>\n" );
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document.write( "* Let 'x' be the amount of Cheese X in pounds.<BR>\n" );
document.write( "* Let 'y' be the amount of Cheese Y in pounds.\r<BR>\n" );
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document.write( "**2. Formulate Constraints**\r<BR>\n" );
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document.write( "* **Weight Constraint:** x + y ≥ 4 (Total weight must be at least 4 pounds)<BR>\n" );
document.write( "* **Sharpness Ingredient Constraint:** 3x + y ≥ 6 (Total amount of ingredient S must be at least 6 ounces)<BR>\n" );
document.write( "* **Constraint on Cheese Y:** y - x ≤ 1 \r<BR>\n" );
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document.write( "**3. Define Objective Function**\r<BR>\n" );
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document.write( "* **Cost Function (to be minimized):** <BR>\n" );
document.write( "    * Cost = 4x + 1y \r<BR>\n" );
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document.write( "**4. Graphical Representation**\r<BR>\n" );
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document.write( "* **Plot the constraints:**<BR>\n" );
document.write( "    * x + y ≥ 4 <BR>\n" );
document.write( "    * 3x + y ≥ 6 <BR>\n" );
document.write( "    * y - x ≤ 1\r<BR>\n" );
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document.write( "* **Find the feasible region:** <BR>\n" );
document.write( "    * The feasible region is the area on the graph that satisfies all the constraints simultaneously.\r<BR>\n" );
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document.write( "* **Identify the corner points of the feasible region.**\r<BR>\n" );
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document.write( "**5. Evaluate the Objective Function at Corner Points**\r<BR>\n" );
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document.write( "* Calculate the cost at each corner point of the feasible region.\r<BR>\n" );
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document.write( "**6. Determine the Minimum Cost**\r<BR>\n" );
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document.write( "* The corner point with the lowest cost value provides the minimum cost of the mixture.\r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* This problem can be solved graphically by plotting the constraints and finding the feasible region. <BR>\n" );
document.write( "* Alternatively, you can use linear programming techniques (such as the simplex method) to find the optimal solution.\r<BR>\n" );
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document.write( "**To find the exact solution, you would need to:**\r<BR>\n" );
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document.write( "1. **Graph the constraints**<BR>\n" );
document.write( "2. **Identify the feasible region**<BR>\n" );
document.write( "3. **Determine the corner points**<BR>\n" );
document.write( "4. **Calculate the cost at each corner point**\r<BR>\n" );
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document.write( "The corner point with the lowest cost will give you the minimum cost of the mixture and the optimal amounts of Cheese X and Cheese Y.<BR>\n" );
document.write( " </SPAN>\n" );
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