document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155593>Question 1155593</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9) A diet specialist tells patient to add oranges and apples to her diet for Vitamin A, Vitamin B, and Vitamin C. A kg (kilogram) of oranges contributes 8 grams of Vitamin C, 6 grams of Vitamin B, and 2 grams of Vitamin A, while a kg of apples contributes 3 grams of Vitamin A and 6 grams of Vitamin B. A kg of oranges costs $1.95 and a kg of apples costs $2.99. The patient has to meet a minimum requirement of 22 grams of Vitamin A, 33 grams of Vitamin B, and 16 grams of Vitamin C. She should avoid taking more than 73 grams of Vitamin A and 64 grams of Vitamin B to avoid side effects such as nausea. Formulate a linear programming problem to help the patient choose the ideal fruit mix for their diet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778206 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</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=778206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A diet specialist tells patient to add oranges and apples to her diet for Vitamin A, Vitamin B, and Vitamin C. \r<BR>\n" );
document.write( "\n" );
document.write( "A kg (kilogram) of oranges contributes 8 grams of Vitamin C, 6 grams of Vitamin B, and 2 grams of Vitamin A, while \r<BR>\n" );
document.write( "\n" );
document.write( "a kg of apples contributes 3 grams of Vitamin A and 6 grams of Vitamin B. \r<BR>\n" );
document.write( "\n" );
document.write( "A kg of oranges costs $1.95 and a kg of apples costs $2.99. \r<BR>\n" );
document.write( "\n" );
document.write( "The patient has to meet a minimum requirement of 22 grams of Vitamin A, 33 grams of Vitamin B, and 16 grams of Vitamin C. \r<BR>\n" );
document.write( "\n" );
document.write( "She should avoid taking more than 73 grams of Vitamin A and 64 grams of Vitamin B to avoid side effects such as nausea. \r<BR>\n" );
document.write( "\n" );
document.write( "Formulate a linear programming problem to help the patient choose the ideal fruit mix for their diet.<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "Let x be the amount of oranges, and let y be the amount of apples for optimal diet (in kilograms).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the objective function to minimize is the price  P = 1.95x + 2.99y  dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The constraints are\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "22 <= 2x + 3y <= 73   (the amount of vitamin A, in grams)\r\n" );
document.write( "\r\n" );
document.write( "33 <= 6x + 6y <= 64   (the amount of vitamin B, in grams)\r\n" );
document.write( "\r\n" );
document.write( "16 <= 8x              (the amount of vitamin C, in grams)\r\n" );
document.write( "\r\n" );
document.write( "x >= 0,  y >= 0.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "The setup is just completed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To see many problems solved by the Linear Programming method, &nbsp;look into the lesson\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/misc/Solving-minimax-problems-by--the-Linear-Programming-method.lesson>Solving minimax problems by the Linear Programming method</A> \r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, &nbsp;look into the solutions of other similar problems in the archive to this forum under the links\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1148776.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1142000.html \r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1137172.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1136382.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.1134444.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1131906.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html   (!)\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1112482.html\r<BR>\n" );
document.write( "\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "/\/\/\/\/\/\/\/\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In order for the formulation be <U>precisely correct</U>, from the common sense point of view,\r<BR>\n" );
document.write( "\n" );
document.write( "it must say for what time period this diet is designed (a day, a week, and so on . . . )\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It does not play any role in the setup and/or in the solution,\r<BR>\n" );
document.write( "\n" );
document.write( "but is NECESSARY PART from the common sense point of view.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );