document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118832>Question 1118832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can some one please check my \"work\"\r<BR>\n" );
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document.write( "a moving company wants to purchase a min of 15 trucks with a load capacity of at least 36 tons. Model a holds 2 tons and costs 15,000 Model b holds 3 toms and costs 24,000 how many of each to minimize costs and what is the cost\r<BR>\n" );
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document.write( "Here is what I have so far\r<BR>\n" );
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document.write( "M= 15A+24B\r<BR>\n" );
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document.write( "A+B=15<BR>\n" );
document.write( "B= -A+15\r<BR>\n" );
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document.write( "2A+3B _> 36 <BR>\n" );
document.write( "B= -2/3A + 12\r<BR>\n" );
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document.write( "Vertexs<BR>\n" );
document.write( "0,15<BR>\n" );
document.write( "9,6<BR>\n" );
document.write( "18,0\r<BR>\n" );
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document.write( "to get lowest cost and min amount of capacity they need to buy 18 \"truck A\" and 0 \"Truck B\"\r<BR>\n" );
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document.write( "is this correct or am I missing a step?<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 #734270 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If you have several problems like this to solve, let me show you something that might save you some time and effort.<br><BR>\n" );
document.write( "The boundary lines of the constraint functions in the problem are<br><BR>\n" );
document.write( "(1) x+y=15  -->  y = -x+15  -->  slope = -1<BR>\n" );
document.write( "(2) 2x+3y=36  -->  y = (-2/3)x+12  -->  slope = -2/3<br><BR>\n" );
document.write( "The objective function boundary line is<br><BR>\n" );
document.write( "(3) 15x+24y=a (a is a constant we don't care about) -->  y = (-5/8)x+b (another constant we don't care about)  -->  slope = -3/5<br><BR>\n" );
document.write( "The slope of the objective function is larger (less negative) than the slope of either objective function.<br><BR>\n" );
document.write( "The corner of the feasibility region where the objective function achieves it minimum value is the corner where a line with slope -3/5 just touches the feasibility region without passing through it.<br><BR>\n" );
document.write( "Referring to the diagram in the response provided by tutor @ikleyn, it is easy to see that the corner where that happens is (18,0).<br><BR>\n" );
document.write( "In this problem, with only two constraints, this method only saves you a small amount of work.  But in a problem with more constraints and therefore many more corners of the feasibility region, it can save you a lot of time, because you know which corner is going to give you the answer.  To get the answer, you will only have to find one of the intersection points of the constraint lines and evaluate the objective function at that one point. </SPAN>\n" );
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