document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077460>Question 1077460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi Audio purchases speakers from a manufacturing company and installs them in its own cabinets. Their model A speaker assembly, which sells for $200 has a tweeter and mid-range speaker. The model B Assembly, which sells for $350, has two tweeters, mid-range and a woofer. Hi Audio currently has in stock 90tweeters, 60 mid-range speakers, and 44 woofers. How many speaker assemblies of each should they make to maximize revenue?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691973 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=691973\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let r = revenue<BR>\n" );
document.write( "let x = number of model A speaker assemblies.<BR>\n" );
document.write( "let y = number of model B speaker assemblies.\r<BR>\n" );
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document.write( "model A speaker has 1 tweeter and 1 mid-range speaker assembly.<BR>\n" );
document.write( "model B speaker has 2 tweeters and 1 mid-range and 1 woofer speaker assembly.\r<BR>\n" );
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document.write( "number of tweeter speaker assemblies in stock is equal to 90.<BR>\n" );
document.write( "number of mid-range speaker assemblies in stock is equal to 60.<BR>\n" );
document.write( "number of woofer speaker assemblies in stock is equal to 44.\r<BR>\n" );
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document.write( "your revenue function is r = 200x + 350y\r<BR>\n" );
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document.write( "this is the function that you want to maximize.\r<BR>\n" );
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document.write( "your constraint functions are:\r<BR>\n" );
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document.write( "x + 2y <= 90 (each model A needs 1 tweeter and each model B needs 2)<BR>\n" );
document.write( "x + y <= 60 (each model A and each model B need 1 mid-range each)<BR>\n" );
document.write( "y <= 44 (each model B needs 1 woofer and each model A doesn't need any)<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "you graph the constraint functions to find the area of feasibility and then you look for the corner points of the feasible region to find the least cost solution.\r<BR>\n" );
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document.write( "using the desmos.com, you would graph the opposite of the inequalities and then look for the area on the graph that is not shaded.\r<BR>\n" );
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document.write( "you would graph the following inequalities:\r<BR>\n" );
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document.write( "x + 2y >= 90 <BR>\n" );
document.write( "x + y >= 60 <BR>\n" );
document.write( "y >= 44 <BR>\n" );
document.write( "x <= 0<BR>\n" );
document.write( "y <= 0\r<BR>\n" );
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document.write( "your graph would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/042001.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "your maximum revenue is when x = 30 and y = 30\r<BR>\n" );
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document.write( "all the constraints are satisfied.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "when x = 30 and y = 30:\r<BR>\n" );
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document.write( "revenue = 30 * 200 + 30 * 350 = 16,500\r<BR>\n" );
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document.write( "number of tweeters = 30 * 1 + 30 * 2 = 90 which is <= 90.\r<BR>\n" );
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document.write( "number of mid-range speaker assemblies = 30 * 1 + 30 * 1 = 60 which is <= 60.\r<BR>\n" );
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document.write( "number of woofers = 30 * 1 = 30 which is <= 44.\r<BR>\n" );
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document.write( "you may check for yourself to determine that the max revenue is when x = 30 and y = 30.\r<BR>\n" );
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document.write( "the other options are:\r<BR>\n" );
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document.write( "x = 0 and y = 44<BR>\n" );
document.write( "x = 2 and y = 44<BR>\n" );
document.write( "x = 60 and y = 0<BR>\n" );
document.write( "x = 0 and y = 0\r<BR>\n" );
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document.write( "desmos.com calculator  can be found at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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