document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199297>Question 1199297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Star Electronics Company produces two robotic vacuums. The production process for each product is similar in that both require a certain number of hours of electronic work and a certain number of labour hours in the assembly department. Robotic vacuum A takes 4 hours of electronic work and 2 hours in the assembly shop. Robotic vacuum B requires 3 hours in electronics and 1 hour in assembly. During the current production period, 240 hours of electronic time are available, and 100 hours of assembly department time are available. Each robotic vacuum A sold yields a profit of RM 700 while each robotic vacuum B produced may be sold for a RM 500 profit.<BR>\n" );
document.write( "Formulate a linear programming model for this problem.\r<BR>\n" );
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document.write( "a)	Find the objective function\r<BR>\n" );
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document.write( "b)	Identify the variable and list all the constraints\r<BR>\n" );
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document.write( "c)	Calculate the intersection point.\r<BR>\n" );
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document.write( "d)	Draw the graph with a complete label of the axis, intersection point, line equation, and shaded region.\r<BR>\n" );
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document.write( "e)	Find the optimal solution<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 #833110 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of type A robotic vacuums.<BR>\n" );
document.write( "y = number of type B robotic vacuums.\r<BR>\n" );
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document.write( "objective function is profit = 700x + 500y<BR>\n" );
document.write( "this is what you want to maximize.\r<BR>\n" );
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document.write( "constraint functions are:\r<BR>\n" );
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document.write( "4x + 3y <= 240 for electronics work hours.<BR>\n" );
document.write( "2x + y = 100 for assembly hours.<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "the chart that i made up is shown below:<BR>\n" );
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document.write( "                              type A        type B\r\n" );
document.write( "electronics work hours           4             3        <= 240\r\n" );
document.write( "assembly hours                   2             1        <= 100\r\n" );
document.write( "profit                         700           500        maximize   \r\n" );
document.write( "</PRE>    \r<BR>\n" );
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document.write( "using the calculator at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blanak\">https://www.desmos.com/calculator</a>, you would graph the opposite of the inequalities.  <BR>\n" );
document.write( "the are of the graph that is not shaded is your region of feasibility.<BR>\n" );
document.write( "your maximum profit will be at the corner points of this region.<BR>\n" );
document.write( "the corner points on the graph are in (x,y) format.<BR>\n" );
document.write( "x represents the number of type A vacuums.<BR>\n" );
document.write( "y represents the number of type B vacuums.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/121901.jpg\">\r<BR>\n" );
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document.write( "the maximum profit is at (30,40) = 41,000<BR>\n" );
document.write( "total electronics hours = 240<BR>\n" );
document.write( "total assembly hours = 100<BR>\n" );
document.write( "all constraints were met.\r<BR>\n" );
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document.write( "let me know if you have any quetions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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