document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162002>Question 1162002</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An accounting firm has 800 hours of staff time and 96 hours of reviewing time available each week. The firm charges 1000 dollars for an audit and 300 dollars for a tax return. Each audit requires 100 hours of staff time and 8 hours of review time. Each tax return requires 12.5 hours of staff time and 2 hours of review time.<BR>\n" );
document.write( "a) What numbers of audits and tax returns will yield the maximum revenue?<BR>\n" );
document.write( "b) What is the maximum revenue? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785685 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=785685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> make a table as shown below.<BR>\n" );
document.write( "this table makes it easier to see how the variables are applied to the problem.<BR>\n" );
document.write( "x = the number of audits.<BR>\n" );
document.write( "y = the number of returns.<BR>\n" );
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document.write( "                           x                    y\r\n" );
document.write( "                           audits               returns\r\n" );
document.write( "staff hours                100                  12.5            <= 800\r\n" );
document.write( "review hours               8                    2               <= 96\r\n" );
document.write( "revenue dollars            1000                 300             maximize\r\n" );
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document.write( "your constraint inequalities are:\r<BR>\n" );
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document.write( "100x + 12.5 <= 800 for staff hours<BR>\n" );
document.write( "8x + 2y <= 96 for review hours\r<BR>\n" );
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document.write( "your objective function is:\r<BR>\n" );
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document.write( "1000x + 300y for revenue dollars that you want to maximize\r<BR>\n" );
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document.write( "using the desmos.com calculator, you graph the opposite of the constraint inequalities.\r<BR>\n" );
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document.write( "you will graph:\r<BR>\n" );
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document.write( "100x + 12.5 <= 800 for staff hours<BR>\n" );
document.write( "8x + 2y <= 96 for review hours\r<BR>\n" );
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document.write( "also graph:\r<BR>\n" );
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document.write( "x <= 0<BR>\n" );
document.write( "y <= 0\r<BR>\n" );
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document.write( "this is because x and y must be greater than or equal to 0 in this problem.\r<BR>\n" );
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document.write( "the area on the graph  that is NOT shaded is the region of feasibility.<BR>\n" );
document.write( "your maximum revenue will be at the corner points of this region.<BR>\n" );
document.write( "you evaluate your objective function at those corner points.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/070502.jpg\" >\r<BR>\n" );
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document.write( "you will find that your maximum revenue is at the point (0,48).<BR>\n" );
document.write( "the revenue is 0x + 300y = 0 + 14,400 = 14,400.<BR>\n" );
document.write( "that means max revenue when you provide zero audits and 48 tax returns for revenue of 14,400 dollars.\r<BR>\n" );
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document.write( "your constraint inequalities need to be satisfied.\r<BR>\n" );
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document.write( "at (0,48), 100x + 12.5y = 600 <= 800, and 8x + 2y = 96 <= 96.\r<BR>\n" );
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document.write( "the constraints are all satisfied.<BR>\n" );
document.write( "your maximum revenue is 14,400.\r<BR>\n" );
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document.write( "you can evaluate the other corner points on your own to confirm that (0,48) give you the maximum revenue.<BR>\n" );
document.write( "the constraints should also be saisfied at those other corner points as well.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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