document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202370>Question 1202370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A food factory is making a beverage for a customer from mixing two different existing products A and B. The compositions of A and B and prices ($/L) are given as follows,<BR>\n" );
document.write( "Amount (L) in /100 L of A and B\r<BR>\n" );
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document.write( "   Lime Orange Mango Cost ($/L)<BR>\n" );
document.write( "A  2    6      4      4<BR>\n" );
document.write( "B  7    4      8      12\r<BR>\n" );
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document.write( "The customer requires that there must be at least 5 Litres (L) Orange and at least 5 Litres of Mango concentrate per 100 Litres of the beverage respectively, but no more than 6 Litres of Lime concentrate per 100 Litres of beverage. The customer needs at least 140 Litres of the beverage per week.\r<BR>\n" );
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document.write( "a) Formulate a Linear Programming (LP) model for the factory that minimises the total cost of producing the beverage while satisfying all constraints.<BR>\n" );
document.write( "b) Use the graphical method to find the optimal solution. Show the feasible region and the optimal solution on the graph. Annotate all lines on your graph.<BR>\n" );
document.write( "c) What is the range for the cost ($) of A that can be changed without affecting the optimum solution obtained above? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837165 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i get 140 liters of beverage A with a cost of 560.<BR>\n" );
document.write( "here's the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/052001.jpg\"><BR>\n" );
document.write( "the cost of A was 4 dollars per liter.<BR>\n" );
document.write( "the coswt of B was 12 dollars per liter.<BR>\n" );
document.write( "the corner points of the feasible region are:<BR>\n" );
document.write( "(76,64) = corner point 1<BR>\n" );
document.write( "(140,0) = corner point 2<BR>\n" );
document.write( "(300,0) = corner point 3<BR>\n" );
document.write( "cost for corner point 1 was 76 * 4 + 64 * 12 = 1072<BR>\n" );
document.write( "cost for corner point 2 was 140 * 4 = 560<BR>\n" );
document.write( "cost for corner point 3 was 300 * 4 = 1200<BR>\n" );
document.write( "sensitivity would be to keep raising the cosw for the x value until the minimum cost changes.<BR>\n" );
document.write( "x is the number of liters of beverage A.<BR>\n" );
document.write( "y is the number of liter of beverage B.<BR>\n" );
document.write( "sensiivity analysis indidcates that the optimum solution will be change when the cost of beverage A increases to more than 12.00 per liter.<BR>\n" );
document.write( "the following excel spreadsheet shows the sensiivity analysis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/052101.jpg\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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