document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76536>Question 76536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours. The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week. Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths. Then graph the system of inequalities.<BR>\n" );
document.write( "Here is what i have so far:<BR>\n" );
document.write( "x=40 items * 1 hour = 40 hours<BR>\n" );
document.write( "y=20 items * 2 hours =40 hours<BR>\n" );
document.write( "So I have the 60 items and the 80 hours, but how do I write a system of inequalities representing this and then how do I graph it. See I'm trying. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54901 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I was actually teaching this to a bunch of first year degree students, only a couple of weeks ago. If you're interested, this is how you begin a linear programming problem. Anyway. The first thing to do is identify our variables - this really only comes with practice, but normally you will find (at least in simple problems) the variables rae normally the things you can make.<br />\r<BR>\n" );
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document.write( "In this case we have the number of bouquets (x) and the number of wreaths (y)<br />\r<BR>\n" );
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document.write( "OK, the bouquests take 1 hour each to produce, and the wreaths take 2, so the amount of time to produce x bouquets and y wreats is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x+2y\"> right? Now, labour is at a maximum of 80 hours so our first inequality is simply<br />\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x+2y\leq 80\">\r<BR>\n" );
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document.write( "The total production capacity is the amount of things we can make, yeah? so if we make x bouquets and y wreaths, then we make x+y things, agreed? We can make a maximum of 60 things so our next inequality is<br />\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x+y\leq 60\">\r<BR>\n" );
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document.write( "WE must also never forget the non-negativity inequalities. Clearly we can't make -5 wreaths or -3 bouquets, so we also have<br />\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x\geq 0\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?y\geq 0\">\r<BR>\n" );
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document.write( "Now you have the inequalities, see if you can graph them. I think someone has written a lesson on here about graphing inequalities, so if you get stuck have a read of that. Or if that fails come back.\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "Kev </SPAN>\n" );
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