document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207812>Question 1207812</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A picnic basket can hold a maximum of 30 apples and 20 sandwiches. Each apple takes up 1 unit of space, and each sandwich takes up 2 units of space. The picnic basket has a total capacity of 60 units of space. What is the maximum number of apples (x) and sandwiches (y) that can be packed?( This is a graphing question so if you read this do you think you could email me and I will send you the pictures of the questions o have 3 questions and if it’s necessary I am willing to pay for it.) Thank you i need the constraints,objetive function, Vertices of possible max./min, solutions, and of course the solution and graph ! Thank you so much ( This is a graphing question so if you read this do you think you could email me and I will send you the pictures of the questions o have 3 questions and if it’s necessary I am willing to pay for it.) Thank you i need the constraints,objetive function, Vertices of possible max./min, solutions, and of course the solution and graph ! Thank you so much  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845925 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52879)</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=845925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A picnic basket can hold a maximum of 30 apples and 20 sandwiches. <BR>\n" );
document.write( "Each apple takes up 1 unit of space, and each sandwich takes up 2 units of space. <BR>\n" );
document.write( "The picnic basket has a total capacity of 60 units of space. <BR>\n" );
document.write( "What is the maximum number of apples (x) and sandwiches (y) that can be packed?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "( This is a graphing question so if you read this do you think you could email me and I will send you the pictures of the questions o have 3 questions and if it’s necessary I am willing to pay for it.) Thank you i need the constraints,objetive function, Vertices of possible max./min, solutions, and of course the solution and graph ! Thank you so much ( This is a graphing question so if you read this do you think you could email me and I will send you the pictures of the questions o have 3 questions and if it’s necessary I am willing to pay for it.) Thank you i need the constraints,objetive function, Vertices of possible max./min, solutions, and of course the solution and graph ! Thank you so much<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will solve it using different method, applying logical reasoning and common sense.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will not make any plots to save my time.\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( "We want maximize the number of apples and sandwiches (more precisely, the sum of them),\r\n" );
document.write( "satisfying the other given constraints.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let's apply the most aggressive strategy.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We will take as much apples as possible (30 apples), since they take only 1 unit of space, each.\r\n" );
document.write( "Then we complement it with appropriate number of sandwiches, which is  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2860-30%29%2F2 ALIGN=MIDDLE  ALT=\"%2860-30%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 15  (the remaining space divided by 2).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the solution is 30 apples and 15 sandwiches, which gives the total of 30 + 15 = 45 items.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that this solution satisfies all the constraints.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Thus we solved the problem easy and elegantly using logical reasoning and common sense.\r<BR>\n" );
document.write( "\n" );
document.write( "No plots are needed.\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( "<BR>\n" );
document.write( "\n" );
document.write( "Outwardly, this problem is similar to Linear Programming problems, <BR>\n" );
document.write( "where the geometric solution method is often used.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But concretely, this particular problem can be easily solved in MUCH SIMPLER WAY<BR>\n" );
document.write( "using simple logic without any plots.  That's why I call such tasks False Linear Programming problems.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "All of your other today's problems belong to the same class/type,<BR>\n" );
document.write( "and can be solved using logic, ONLY.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In my view, this simple logical solution is much more valuable solution method for the given problem\r<BR>\n" );
document.write( "\n" );
document.write( "than to apply heavy artillery of the Linear Programming method blindly and without necessity.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );