document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071240>Question 1071240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2 A small manufacturer produces two kinds of good, A and B, for which demand exceeds capacity. The production costs for A and B are $6 and $3, respectively, each, and the corresponding selling prices are $7 and $4. In addition, the transport costs are 20 cents and 30 cents for each good of type A and B, respectively. The conditions of a bank loan limit the manufacturer to maximum weekly production costs of $2700 and maximum weekly transport costs of $120.<BR>\n" );
document.write( "How should the manufacturer arrange production to maximize profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686170 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=686170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of units of product A.<BR>\n" );
document.write( "y = number of units of product B.\r<BR>\n" );
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document.write( "your constraint inequalitiess are:\r<BR>\n" );
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document.write( "x >= 0<BR>\n" );
document.write( "y >= 0<BR>\n" );
document.write( "6x + 3y <= 2700<BR>\n" );
document.write( ".2x + .3y <= 120\r<BR>\n" );
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document.write( "selling price is equal to 7x + 4y\r<BR>\n" );
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document.write( "profit is equal to 7x - 6x - .2x + 4y - 3y - .3y\r<BR>\n" );
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document.write( "combine like terms and you get:\r<BR>\n" );
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document.write( "profit is equal to .8x + .7y\r<BR>\n" );
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document.write( "that's your objective function.\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would graph the opposite inequalities.\r<BR>\n" );
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document.write( "to be more specific, you would graph the following inequalities.\r<BR>\n" );
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document.write( "x <= 0<BR>\n" );
document.write( "y <= 0<BR>\n" );
document.write( "6x + 3y >= 2700<BR>\n" );
document.write( ".2x + .3y >= 120\r<BR>\n" );
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document.write( "the area of the graph that is NOT shaded is your region of feasibility.\r<BR>\n" );
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document.write( "your graph will look like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/030301.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you then find the corner points of this region and evaluate your objective function at those corner points.\r<BR>\n" );
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document.write( "you will get.\r<BR>\n" );
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document.write( "profit at (0,400) = 280<BR>\n" );
document.write( "profit at (375,150) = 405<BR>\n" );
document.write( "profit at (450,0) = 360\r<BR>\n" );
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document.write( "your maximum profit is at (375,150).\r<BR>\n" );
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document.write( "you have to meet your constraints at those corner points.\r<BR>\n" );
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document.write( "production costs at (375,150) = 6x + 4y = 2700 which meets the constraint that they be less than or equal to 2700.\r<BR>\n" );
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document.write( "transport costs at (375,150) = .2x + .3y = 120 which meets the constraint that they be less than or equal to 120.\r<BR>\n" );
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document.write( "x >= 0 and y >= 0 are also meet the constraint that they be greater than or equal to 0 at the point (375,150).\r<BR>\n" );
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document.write( "all constraints are met.\r<BR>\n" );
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document.write( "your maximum profit is when you sell 375 units of product A and 150 units of product B.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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