document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200944>Question 1200944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> QUESTION ONE <BR>\n" );
document.write( "a)	Elaborate the assumptions underlying linear programming model  <BR>\n" );
document.write( "b)	Explain the steps that are taken during decision making process                                                      <BR>\n" );
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document.write( "QUESTION TWO <BR>\n" );
document.write( "A firm is engaged in producing two products A and B, each unit of product A requires 2 kg of row material and 4 labour hours for processing, whereas each unit of product B requires 3 kg of row material and 3 hours of labour of the same type. Every week, the firm has an availability of 60 kg of row material and 96 labour hours. One unit of product A sold yields $ 40 and one unit of product B sold gives $35 as profit. <BR>\n" );
document.write( "Required: Formulate this problem as a linear programming problem to determine as to how many units of each of the products should be produd  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835381 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=mananth&illustration_name=LP.png\">.<BR>\n" );
document.write( "Let number of units of A be x and that of B be y\r<BR>\n" );
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document.write( "Raw Material<BR>\n" );
document.write( "Product A Raw material = 2kg<BR>\n" );
document.write( "Product B raw material =3kg<BR>\n" );
document.write( "Available Raw material 60 kg per week\r<BR>\n" );
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document.write( "Labour <BR>\n" );
document.write( "Product A  4hours <BR>\n" );
document.write( "Product B 3 hours<BR>\n" );
document.write( "Total hours avaiable = 96\r<BR>\n" );
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document.write( "We can formulate two equations as follows<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y+%3C=+60 ALIGN=MIDDLE  ALT=\"2x%2B3y+%3C=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" >     When x = 0, y=20 (0,20) When y=0, x=30 (30,0)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y+%3C=+96 ALIGN=MIDDLE  ALT=\"4x%2B3y+%3C=+96\"   DISABLED_style= \"max-width:90%; height:auto;\" >     When x=0 y=32 (0,32)   when y=0 x=24    (24,0) <BR>\n" );
document.write( "Profit be z<BR>\n" );
document.write( "z=40x+35y<BR>\n" );
document.write( "The feasible area is the shaded portion.<BR>\n" );
document.write( "The points are O (0,0) C(24,0), P(18,8) ,D (0,32)<BR>\n" );
document.write( "z=40x+35y<BR>\n" );
document.write( "At O z=0<BR>\n" );
document.write( "At C , 24*40+35*0 =960<BR>\n" );
document.write( "At P 40*18+35*8= 1000<BR>\n" );
document.write( "At D 40*0 +32*35= 700<BR>\n" );
document.write( "At P(18,8) we get maximum output <BR>\n" );
document.write( "18 units of A and 8 units of B\r<BR>\n" );
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