document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106875>Question 1106875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a stereo manufacturer has two warehouses labeled I and II. Warehouse I has nine speakers in stock while warehouse II has five. The manufacturer receives orders from customer a for 7 speakera and from customer b for 6 speakers. the shipping rates to send one speaker to cust a is $11 from warehouse and $15 from warehouse II. Cost for customer B is $12 per speaker from warehouse I and $13 from warehouse II. How many speakers should be sent from each warehouse to each customer so that the order is filled for the smallest cost? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721995 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=721995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> make a cost matrix like the one shown below:\r<BR>\n" );
document.write( "\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" );
document.write( "                           warehouse 1       warehouse 2\r\n" );
document.write( "\r\n" );
document.write( "     customer A               11                15\r\n" );
document.write( "     customer B               12                13\r\n" );
document.write( "\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the maximum number of speakers from warehouse 1 is 9.<BR>\n" );
document.write( "the maximum number of speakers from warehouse 2 is 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it's clear from this matrix that the minimum cost to ship to customer A is from warehouse 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since customer A requires 7 and warehouse 1 has 9, then ship all stereos to customer A from warehouse 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the cost to ship to customer B is cheaper from warehouse 1, then ship the remaining 2 that warehouse 1 has to customer B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the remaining 4 that customer B requires is then shipped from warehouse 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your total cost will be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "7 from warehouse 1 to customer A = 77 <BR>\n" );
document.write( "2 from warehouse 1 to customer A = 24<BR>\n" );
document.write( "4 from warehouse 2 to customer B = 52\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total cost is 153.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cheapest cost to ship is 153.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i then double checked to see if my logic was correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used excel solver.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "excel confirmed that my logic was correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it came up with the same minimum cost.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the variables that i used were:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "xa = amount shipped from warehouse 1 to customer a.<BR>\n" );
document.write( "xb = amount shipped from warehouse 1 to customer b.<BR>\n" );
document.write( "ya = amount shipped from warehouse 2 to customer a.<BR>\n" );
document.write( "yb = amount shipped from warehouse 2 to customer b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the objective function which i wanted to minimize was:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "xa * 11 + xb * 12 + ya * 15 + yb * 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this objective function represented the total cost of shipping.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "my constraints were:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "xa + ya = 7 because customer a required 7 speakers.<BR>\n" );
document.write( "xb + yb = 6 because customer b required 6 speakers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "xa + xb <= 9 because warehouse 1 could ship a maximum of 9 speakers.<BR>\n" );
document.write( "ya + yb <= 5 because warehouse 2 could ship a maximum of 5 speakers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a picture of my excel spreadsheet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/012001.jpg\" alt=\"$$$\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );