document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186852>Question 1186852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> LINEAR PROGRAMMING\r<BR>\n" );
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document.write( "The campus store sells dessert, Sobolo drink and Brukina drink. The Sobolo cost GH₵1.90 and the Brukina cost GH₵2.25. They sell the Sobolo drink for GH₵5.00 and the Burukina for GH₵6.00. They can obtain no more than 100 Sobolo and 75 Burukina per week. To meet the demands, they have to sell a total of at least 120 of the two drinks together. They cannot package more than 150 per week. <BR>\n" );
document.write( "(i)	Formulate this problem in terms of determining the profit- maximizing combination of the two drinks.                                                                             \r<BR>\n" );
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document.write( "(ii)	Solve the problem graphically.                                                         \r<BR>\n" );
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document.write( "(iii)	How many of each should they sell to maximize profit?                 \r<BR>\n" );
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document.write( "(iv)	Which constraints are binding?                                                        \r<BR>\n" );
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document.write( "(v)	Determine the slack materials  \r<BR>\n" );
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document.write( "(vi)	Interpret your answers obtained in (v) above.                                                                                           \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 #849341 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</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=849341\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "LINEAR PROGRAMMING\r<BR>\n" );
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document.write( "The campus store sells dessert, Sobolo drink and Brukina drink. <BR>\n" );
document.write( "The Sobolo cost GH₵1.90 and the Brukina cost GH₵2.25. <BR>\n" );
document.write( "They sell the Sobolo drink for GH₵5.00 and the Brukina for GH₵6.00. <BR>\n" );
document.write( "They can obtain no more than 100 Sobolo and 75 Brukina per week. <BR>\n" );
document.write( "To meet the demands, they have to sell a total of at least 120 of the two drinks together. <BR>\n" );
document.write( "They cannot package more than 150 per week. <BR>\n" );
document.write( "(i)	Formulate this problem in terms of determining the profit- maximizing combination of the two drinks.                                                                             \r<BR>\n" );
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document.write( "(ii)	Solve the problem graphically.                                                         \r<BR>\n" );
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document.write( "(iii)	How many of each should they sell to maximize profit?                 \r<BR>\n" );
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document.write( "(iv)	Which constraints are binding?                                                        \r<BR>\n" );
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document.write( "(v)	Determine the slack materials  \r<BR>\n" );
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document.write( "(vi)	Interpret your answers obtained in (v) above.                                                                                           <BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem is very simple and admits very simple MENTAL solution.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This mental solution is much more educative than formal Linear Programming solution.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Therefore, I place here this mental solution, which require common sense and nothing more.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "One Sobolo drink creates the profit of  5.00-1.90 = 3.10.\r\n" );
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document.write( "One Brukina drink creates the profit of 6.00-2.25 = 3.75.\r\n" );
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document.write( "So, let's apply the most aggressive strategy: will sell Brukina drinks as many as possible \r\n" );
document.write( "in accordance with constraints, and then will sell Sobolo drinks as many as possible\r\n" );
document.write( "in accordance with the remaining constraints.\r\n" );
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document.write( "According to constraints, we can solve 75 Brukina and we can not solve more Brukina due to the constrain 75.\r\n" );
document.write( "OK, so we sell 75 Brukina.\r\n" );
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document.write( "Then the other constrain (150 for both) says that we can sell only 75 = 150 - 75 Sobolo.\r\n" );
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document.write( "It meets another constraint for Sobolo and for both, so we are OK to do it.\r\n" );
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document.write( "Thus the optimal solution is 75 Brukina and 75 Sobolo, that give the total profit of \r\n" );
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document.write( "    75*(3.10 + 3.75) = 513.75.\r\n" );
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document.write( "All other constraints are satisfied.\r\n" );
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document.write( "<U>ANSWER</U>.  The optimal solution is 75 Brukina and 75 Sobolo, that give the total profit of GH₵513.75.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "To further mock the authors, I will notice that in one part of the problem's condition they use the name Brukina,<BR>\n" );
document.write( "while in other part of problem's condition they use the name Burukina, so I conclude <BR>\n" );
document.write( "that they do not know the right name, and moreover, using a consistent name is not their priority.\r<BR>\n" );
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document.write( "To be consistent, I used the name Brukina consistently in the course of my solution.\r<BR>\n" );
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