document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194469>Question 1194469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Star Electronics Company produces two robotic vacuums.<BR>\n" );
document.write( "The production process for each product is similar in that <BR>\n" );
document.write( "both require a certain number of hours of electronic work <BR>\n" );
document.write( "and a certain number of labour hours in the assembly <BR>\n" );
document.write( "department. Robotic vacuum A takes 4 hours of electronic <BR>\n" );
document.write( "work and 2 hours in the assembly shop.  Robotic vacuum B <BR>\n" );
document.write( "requires 3 hours in electronics and 1 hour in assembly. <BR>\n" );
document.write( "During the current production period, 240 hours of <BR>\n" );
document.write( "electronic time are available, and 100 hours of assembly <BR>\n" );
document.write( "department time are available. Each robotic vacuum A sold<BR>\n" );
document.write( "yields a profit of RM 700 while each robotic vacuum B <BR>\n" );
document.write( "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, <BR>\n" );
document.write( "intersection point, line equation, and shaded region.\r<BR>\n" );
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document.write( "e)	Find the optimal solution\r<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 #826684 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20067)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The currency RM is the Malaysian ringgit, which is worth <BR>\n" );
document.write( "about 23 cents in US currency.<BR>\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" );
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document.write( "Vacuums|  A |  B |\r\n" );
document.write( "-------|----|----|limits\r\n" );
document.write( "Number |  x |  y |  ↓\r\n" );
document.write( "-------|----|----|------\r\n" );
document.write( "E. hrs.| 4x | 3y | 240 |\r\n" );
document.write( "-------|----|----|-----|\r\n" );
document.write( "A. hrs.| 2x | 1y | 100 |\r\n" );
document.write( "-------|----|----|------\r\n" );
document.write( "Profit |700x|500y|\r\n" );
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document.write( "Maximize P = 700x + 500y  <--objective function\r\n" );
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document.write( "Subject to constraints:\r\n" );
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document.write( "4x + 3y ≤ 240\r\n" );
document.write( "2x +  y ≤ 100\r\n" );
document.write( "x ≥ 0, y ≥ 0\r\n" );
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document.write( "We draw the graphs of the two lines,\r\n" );
document.write( "Put = in place of ≤\r\n" );
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document.write( "                   Intercepts\r\n" );
document.write( "4x + 3y = 240    (0,80), (60,0)\r\n" );
document.write( "2x +  y = 100   (0,100), (50,0)\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C560%2C-2%2C8%2C-2%2C12%2C%0D%0Alocate%28-.6%2C0%2C%22%280%2C0%29%22%29%2Clocate%284.8%2C0%2C50%29%2Clocate%285.8%2C0%2C60%29%2Clocate%28-.5%2C8.1%2C80%29%2C+locate%28-.7%2C10.1%2C100%29%2Clocate%283%2C4.3%2C%22%2830%2C40%29%22%29%2Clocate%288%2C0%2Cx%29%2C+locate%28-.3%2C12.1%2Cy%29%2C%0D%0Ared%28locate%281%2C3%2Cmatrix%282%2C1%2CSHADED%2CREGION%29%29%29%2C%0D%0Agreen%28line%280%2C8%2C0%2C12%29%2Cline%285%2C0%2C11%2C0%29%2Cline%280%2C10%2C3%2C4%29%2Cline%283%2C4%2C6%2C0%29%29%2C%0D%0A+%0D%0Ared%28line%280%2C8%2C3%2C4%29%2Cline%283%2C4%2C5%2C0%29%2Cline%280%2C0%2C0%2C8%29%2Cline%280%2C0%2C5%2C0%29%29%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( " Corner |\r\n" );
document.write( " point  |    P = 700x + 500y\r\n" );
document.write( "--------|----------------------------------------------\r\n" );
document.write( "  (0,0) |      700(0) + 500(0)  =     0 +     0 =     0\r\n" );
document.write( " (50,0) |     700(50) + 500(0)  = 35000 +     0 = 35000\r\n" );
document.write( "(30,40) |     700(30) + 500(40) = 21000 + 20000 = 41000 <--max. profit\r\n" );
document.write( " (0,80) |      700(0) + 500(80) =     0 + 40000 = 40000 \r\n" );
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document.write( "Optimum solution: Make 30 A's and 40 B's with a max profit of RM 41000\r\n" );
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document.write( "Edwin</PRE><BR>\n" );
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