document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150008>Question 1150008</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A florist designs two high-profit arrangements— a funeral wreath and a bridal centerpiece. The company’s employees can complete up to 15 arrangements each day using up to 24 total person-hours of labor. It takes 4 person-hours to complete 1 funeral wreath, and 1 person-hour to complete 1 bridal centerpiece. How many of each type of arrangements should the florist produce daily for maximum profit, if the profit on a funeral wreath is $60 and the profit on a bridal centerpiece is $48?\r<BR>\n" );
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document.write( "Number of bridal centerpieces <BR>\n" );
document.write( "Number of funeral wreaths  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771415 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52914)</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=771415\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It seems strange to me how &nbsp;@Theo presented his solution.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;I came to solve the problem and to present it in the way in how it &nbsp;SHOULD &nbsp;BE &nbsp;done.\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( "Let x = # funeral wreath,\r\n" );
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document.write( "    y = # bridal centerpieces.\r\n" );
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document.write( "The profit function (which is the objective function in this problem) is \r\n" );
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document.write( "    F(x,y) = 60x + 48y  dollars.\r\n" );
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document.write( "The restrictions are\r\n" );
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document.write( "    x + y <= 15        (arrangements)\r\n" );
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document.write( "    4x + y <= 24       (person-hours)\r\n" );
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document.write( "    x >= 0, y >= 0.\r\n" );
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document.write( "The feasible region is shown in the Figure 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+-2%2C+20%2C+-2%2C+20%2C%0D%0A++++++++++15-x%2C+24-4x%0D%0A%29 ALIGN=MIDDLE  ALT=\"graph%28+330%2C+330%2C+-2%2C+20%2C+-2%2C+20%2C%0D%0A++++++++++15-x%2C+24-4x%0D%0A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "    Lines  x + y = 15 (red)  and  4x + y = 24\r\n" );
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document.write( "The feasible region is the quadrilateral in QI, under the green and the red lines.\r\n" );
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document.write( "It has vertices\r\n" );
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document.write( "      P1 = (0,0)\r\n" );
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document.write( "      P2 = (0,15)    y-intercept of red line;\r\n" );
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document.write( "      P3 = (3,12)    intersection of red and green lines\r\n" );
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document.write( "      P4 = (6,0)     x-intercept of green line.\r\n" );
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document.write( "The values of the objective function at the vertices are\r\n" );
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document.write( "      P1 :    F(0,0)   = 60*0 + 48*0 =    0;\r\n" );
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document.write( "      P2 :    F(0,15)  = 60*0 + 48*15 = 720;\r\n" );
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document.write( "      P3 :    F(3,12)  = 60*3 + 48*12 = 756;\r\n" );
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document.write( "      P4 :    F(15,0)  = 60*5 + 48*0  = 300.\r\n" );
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document.write( "The maximum value of the objective function (of the profit) is achieved at point P3.\r\n" );
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document.write( "Hence, this point gives the solution to the problem.\r\n" );
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document.write( "The maximum profit is achieved if the company produces 3 funeral wreath and 12 bridal centerpieces per day.\r\n" );
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document.write( "The maximum profit then is  756 dollars.\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/Linear-equations/Linear-equations.faq.question.1148776.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1142000.html \r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1137172.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1136382.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.1134444.html\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/playground/test.faq.question.1112482.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( " </SPAN>\n" );
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