document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134444>Question 1134444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ACME company makes two types of rings: the VIP and the SST. They can produce up<BR>\n" );
document.write( "to 24 rings every day using up to 60 total man-hours. It takes 3 man-hours to make one VIP<BR>\n" );
document.write( "ring and 2 man-hours to make one SST ring. How many of each type of ring should be made<BR>\n" );
document.write( "daily to maximize the company’s profit if the profit on the VIP ring is $40 and on the SST ring is<BR>\n" );
document.write( "$35. Show the graph, all equations and work.\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751840 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</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=751840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "Let  X = # of the VIP rings, and\r\n" );
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document.write( "     Y = # of the SST rings.\r\n" );
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document.write( "Then the problem is to maximize the objective (=the profit) function  \r\n" );
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document.write( "    P(X,Y) = 40X + 35Y\r\n" );
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document.write( "under these restrictions\r\n" );
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document.write( "    X + Y <= 24,\r\n" );
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document.write( "    3X + 2Y <= 60,\r\n" );
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document.write( "    X >= 0,  Y >= 0.\r\n" );
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document.write( "The feasibility domain is shown at the plot below.\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-5%2C+30%2C+-5%2C+30%2C%0D%0A++++++++++24-x%2C+%2860-3x%29%2F2%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "    Plot X + y = 24 red),  3x + 2y = 60 (green)\r\n" );
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document.write( "It is the quadrilateral in QI under the red and green lines.\r\n" );
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document.write( "Corner points are  \r\n" );
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document.write( "     P1 = (0,24)     (red line y-interception);\r\n" );
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document.write( "     P2 = (12,12)    (intersection the red and the green lines);\r\n" );
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document.write( "     P3 = (20,0)     (green line x-interception).\r\n" );
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document.write( "Calculate the profit function at the corner points\r\n" );
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document.write( "     P1:  P(0,24)  = 40*0  + 35*24 = 840;\r\n" );
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document.write( "     P2:  P(12,12) = 40*12 + 35*12 = 900;\r\n" );
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document.write( "     P3:  P(20,0)  = 40*20 + 35*0  = 800.\r\n" );
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document.write( "The maximum value is at P2.\r\n" );
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document.write( "Hence, the solution is the point P2 with  X= 12 (the number of the VIP rings)  and  Y = 12 (the number of the SST rings)  \r\n" );
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document.write( "                       and the profit value of  900 dollars.    <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "----------------\r<BR>\n" );
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document.write( "To see other similar problems solved by the Linear Programming method, &nbsp;look into the lesson\r<BR>\n" );
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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" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;look into the solutions of other similar problems in the archive to this forum under the links\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1131906.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1128383.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html\r<BR>\n" );
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document.write( "/\/\/\/\/\/\/\/\r<BR>\n" );
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document.write( "I want to remind you that as an educated visitor, you MUST express your thanks to EACH the solution\r<BR>\n" );
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document.write( "that I produce in response to your request.\r<BR>\n" );
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document.write( "I forced to make this reminder because MANY (if not all) visitors IGNORE THIS RULE.  Unfortunately.\r<BR>\n" );
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document.write( "Which I consider as an extreme degree of discourtesy.\r<BR>\n" );
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