document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154669>Question 1154669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company is planning to buy new fork hoists for material handling, there are two models that will serve their needs, Model M & model R. The warehouse supervisor feels that a minimum of 3 model M hoists and 5 model R hoist will be needed. The supplier has 8 model M hoist and 10 model R hoist on hand for delivery. The company purchasing agent has decided that no more than 14 hoists can be purchased. Model M can handle 12,000 kilograms per hour and model R can handle 10,000 kilograms per hour.   What number of hoist of each model should be purchased for maximum weight handling capacity? What is the maximum weight handling capacity? <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 #777141 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=777141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's your answer two ways.<BR>\n" );
document.write( "first uses a simplex method tool.<BR>\n" );
document.write( "second uses graphical method.<BR>\n" );
document.write( "both give you the same answer.<BR>\n" );
document.write( "max capacity is 156000 kilograms using 8 type M and 6 type R.<BR>\n" );
document.write( "simplex method tool can be found at <BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.zweigmedia.com/RealWorld/simplex.html\" target = \"_blank\">https://www.zweigmedia.com/RealWorld/simplex.html</a><BR>\n" );
document.write( "graphing calculator can be found at:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a><BR>\n" );
document.write( "your objective function is c = 12000x + 10000y<BR>\n" );
document.write( "c stands for capacity.<BR>\n" );
document.write( "x represents type M<BR>\n" );
document.write( "y represents type R<BR>\n" );
document.write( "your constraint functions are:<BR>\n" );
document.write( "x >= 3<BR>\n" );
document.write( "y >= 5<BR>\n" );
document.write( "x <= 8<BR>\n" );
document.write( "y <= 10<BR>\n" );
document.write( "x + y <= 14<BR>\n" );
document.write( "using the desmos.com/calculator you graph the opposite of the inequalities.<BR>\n" );
document.write( "you can see the functions used there.<BR>\n" );
document.write( "you then find the unshaded portion of the graph and you look at the corner points to find the maximum capacity by evaluating each corner point using the objective function.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "at the point (8,6), you get 12000 * * + 10000 * 6 = 156000<BR>\n" );
document.write( "here's the results from using both methods.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/032801.jpg\" alt=\"$$$\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/032802.jpg\" alt=\"$$$\" > </SPAN>\n" );
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