document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181787>Question 181787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi tutors! <BR>\n" );
document.write( "I'm really stuck on this!! \r<BR>\n" );
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document.write( "an orchandist has 10 hectares of land available for growing Fuji apples and Nashi pears. She estimates that each hectare of apples will cost $5000 to establish, and each heactare of pears will cost $20 000 to establish. She is not able to spend more than $100 000 on establishing the orchard. \r<BR>\n" );
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document.write( "It is also estimated that the profit per hectare from apples will be $4000 and the profit per hectare from pears will be $8000.\r<BR>\n" );
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document.write( "What is the maximum profit the orchard can expect? <BR>\n" );
document.write( "How many hectares of Fuji apples and Nashi pears should she plant to achieve this? Show your working clearly. You should explain the reason behind the answer you give.\r<BR>\n" );
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document.write( "This is a huge problem. Sorry about this tutors!! But would appreciate if you could solve it for me!!\r<BR>\n" );
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document.write( "Thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136381 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=136381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> an orchandist has 10 hectares of land available for growing Fuji apples and Nashi pears.<BR>\n" );
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document.write( "Land Inequality: A + P <= 10<BR>\n" );
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document.write( "She estimates that each hectare of apples will cost $5000 to establish, and each heactare of pears will cost $20 000 to establish. She is not able to spend more than $100 000 on establishing the orchard.<BR>\n" );
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document.write( "Cost: P <= 100,000/20,000 = 5<BR>\n" );
document.write( "Cost: A <= 100,000/5000 = 20<BR>\n" );
document.write( "Cost Inequality: 5000A + 20000P <= 100,000<BR>\n" );
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document.write( "It is also estimated that the profit per hectare from apples will be $4000 and the profit per hectare from pears will be $8000.<BR>\n" );
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document.write( "Object Function:<BR>\n" );
document.write( "Profit = 4000A + 8000P<BR>\n" );
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document.write( " <BR>\n" );
document.write( "What is the maximum profit the orchard can expect? <BR>\n" );
document.write( "How many hectares of Fuji apples and Nashi pears should she plant to achieve this? Show your working clearly. You should explain the reason behind the answer you give.<BR>\n" );
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document.write( "Simplify the Inequalities:<BR>\n" );
document.write( "0<= P <=5<BR>\n" );
document.write( "0<= A <=20<BR>\n" );
document.write( "Land: A <= -P + 10<BR>\n" );
document.write( "Cost: A <= -40P + 20<BR>\n" );
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document.write( "Graphing: Let A be the vertical axis and P be the horizontal axis.<BR>\n" );
document.write( "Draw a horizontal line at P=5<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C30%2C-10%2C30%2C5%2C-x%2B10%2C-4x%2B20%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C30%2C-10%2C30%2C5%2C-x%2B10%2C-4x%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Shade the area in the 1st quadrant that satisfies all of the inequalities.<BR>\n" );
document.write( "Find the vertices of that shaded area relating A and P.<BR>\n" );
document.write( "(0,5),(5,5),(5,0),(0,0)<BR>\n" );
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document.write( "Test each of these in the Object Function:<BR>\n" );
document.write( "Profit = 4000A + 8000P<BR>\n" );
document.write( "(0,5): P = 0 + 40,000 = $40,000<BR>\n" );
document.write( "(5,5): P = 20,000 + 40,000 = $120,000<BR>\n" );
document.write( "(5,0): P = 5*4000+0 = $20,000<BR>\n" );
document.write( "(0,0): P = 0 + 0 = $0<BR>\n" );
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document.write( "Conclusion: Maximum profit comes when 5 hectares of apples are planted and <BR>\n" );
document.write( "5 hectares of pears are planted.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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