document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180597>Question 1180597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer has available 300 hours of labour per week and 800 tons of fertilizer, and he has a maximum of 26 acres for strawberries and 37 acres for tomatoes. An acre of strawberries requires 10 hours of labour and 8 tons of fertilizer, whereas an acre of tomatoes requires 3 hours of labour and 20 tons of fertilizer. The profit from an acre of strawberries is $40,000 and the profit from an acre of tomatoes is $30,000. The farmer wants to know the number of acres of strawberries and tomatoes to plant to maximize profit.<BR>\n" );
document.write( "a.	Formulate a linear programming model for this problem.        (7 marks)<BR>\n" );
document.write( "b.	Solve this model by using graphical analysis.		   (8 marks)<BR>\n" );
document.write( "c.	What would be the effect on the number of acres of strawberries and tomatoes to plant, and the maximum profit if the profit from an acre of strawberries was $50,000 instead of $30,000?    	<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 #810419 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A farmer has available 300 hours of labour per week and 800 tons of fertilizer, and he has a maximum of 26 acres for strawberries and 37 acres for tomatoes.<BR>\n" );
document.write( " An acre of strawberries requires 10 hours of labour and 8 tons of fertilizer, whereas an acre of tomatoes requires 3 hours of labour and 20 tons of fertilizer.<BR>\n" );
document.write( " The profit from an acre of strawberries is $40,000 and the profit from an acre of tomatoes is $30,000. The farmer wants to know the number of acres of strawberries and tomatoes to plant to maximize profit.<BR>\n" );
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document.write( "a. Formulate a linear programming model for this problem. (7 marks)<BR>\n" );
document.write( "Let x = no. of acres of strawberries<BR>\n" );
document.write( "let y = no. of acres of tomatoes <BR>\n" );
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document.write( "The acre restraints<BR>\n" );
document.write( "x =< 26<BR>\n" );
document.write( "y =< 37<BR>\n" );
document.write( "the labor equation, arrange both so we can graph it<BR>\n" );
document.write( "10x + 3y = 300<BR>\n" );
document.write( "3y = -10x + 300<BR>\n" );
document.write( "y = (-10/3)x + 100<BR>\n" );
document.write( "the amt of fertilizer equation<BR>\n" );
document.write( "8x + 20y = 800<BR>\n" );
document.write( "20y = -8x + 800<BR>\n" );
document.write( "x = = -.4x + 40<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b. Solve this model by using graphical analysis. (8 marks)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-50%2C+100%2C+-50%2C+100%2C+%28-10%2F3%29x%2B100%2C+-.4x%2B40%2C+37%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "green is fertilizer equation, red is labor, and blue is the tomato constraint<BR>\n" );
document.write( "A vertical line at x=26, should be there for the strawberry constraint, but unable to draw that<BR>\n" );
document.write( "intersection occurs at x=21, y=30<BR>\n" );
document.write( "21 acres of strawberries yields, 21*40000 = $840000<BR>\n" );
document.write( "30 acres of tomatoes  yields,  30 * 30000 = $900000<BR>\n" );
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document.write( "The maximum profit with these two crops : $1740000<BR>\n" );
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document.write( "c. What would be the effect on the number of acres of strawberries and tomatoes to plant, and the maximum profit if the profit from an acre of strawberries was $50,000 instead of $30,000?---wasn't it $40000.<BR>\n" );
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document.write( "Using the graph, If you planted the max, 26 acres of strawberries,<BR>\n" );
document.write( "you could only plant 13 acres of tomatoes:<BR>\n" );
document.write( " 26(50000) + 13(30000) = $169000 profit<BR>\n" );
document.write( "however using the same acreage 21 and 30<BR>\n" );
document.write( "21(50000) + 30(30000) = 1140000 would be max profit<BR>\n" );
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