document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92178>Question 92178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A nursery uses two brands of fertilizer for rose bushes. Brand A costs $3 per pound and provides 280 units of nutrients per pound. Brand B costs $4 per pound and provides 180 units of nutrients per pound. <BR>\n" );
document.write( "CONSTRAINTS: The nursery spends $100 or less for fertilizer and wants to provide at least 5200 units of nutrients. Because brand B contains a special nutrient that brand A does not, the nursery uses at least 4 pounds of brand B. \r<BR>\n" );
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document.write( "How many pounds of each should the nursery use to minimize cost? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67018 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=67018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A nursery uses two brands of fertilizer for rose bushes. <BR>\n" );
document.write( "Brand A costs $3 per pound and provides 280 units of nutrients per pound. <BR>\n" );
document.write( "Brand B costs $4 per pound and provides 180 units of nutrients per pound.<BR>\n" );
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document.write( "CONSTRAINTS: The nursery spends $100 or less for fertilizer and wants to provide at least 5200 units of nutrients. <BR>\n" );
document.write( "Because brand B contains a special nutrient that brand A does not, the nursery uses at least 4 pounds of brand B. <BR>\n" );
document.write( "How many pounds of each should the nursery use to minimize cost? <BR>\n" );
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document.write( "Cost Inequality: 3A + 4B <=100<BR>\n" );
document.write( "Nutrient Inequality: 280A + 180B >=5200<BR>\n" );
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document.write( "Constraints:<BR>\n" );
document.write( "B>=4<BR>\n" );
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document.write( "Solve where you can for B:<BR>\n" );
document.write( "B <=(-3/4)A+25<BR>\n" );
document.write( "B >=(-280/180)A + (5200/180)<BR>\n" );
document.write( "B >=4<BR>\n" );
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document.write( "Plot the last two on an A-B coordinate system<BR>\n" );
document.write( "Find the coordinates of the vertices of the enclosed area.<BR>\n" );
document.write( "Evaluate the cost function with those coordinates to find<BR>\n" );
document.write( "the minimum cost.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-5%2C40%2C-5%2C30%2C%28-14%2F9%29x%2B%28260%2F9%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-5%2C40%2C-5%2C30%2C%28-14%2F9%29x%2B%28260%2F9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the cost equation as your objective function.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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