document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166842>Question 1166842</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello this is our activity in the school but my teacher is not good at explaining. Please help me with the solution. Thankyou. \r<BR>\n" );
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document.write( "The Atlas Fertilizer Company has two plants where the products are made. In a week, plant A can <BR>\n" );
document.write( "make at most 40 tons of fertilizers and plant B can make at most 50 tons of fertilizer per week. The <BR>\n" );
document.write( "production manager wants to make a total of at least 70 tons of fertilizers per week. The amount of <BR>\n" );
document.write( "particulate matter in the atmosphere over the nearby town is measured weekly and found to be 20 <BR>\n" );
document.write( "pounds for each ton of product made in plant A and 40 pounds for each ton of product made in plant <BR>\n" );
document.write( "B. How many tons should be made weekly in each plant to minimize the total amount of particulate <BR>\n" );
document.write( "matter in the atmosphere?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791695 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=791695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this looks like a linear programming type problem.<BR>\n" );
document.write( "it can be solved graphically as long as there are only two unknown variables involved.\r<BR>\n" );
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document.write( "need an objective function and some constraint functions.\r<BR>\n" );
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document.write( "let x = the maximum number of tons of fertilizer from plant A each week.<BR>\n" );
document.write( "let y = the maximum number of tons of fertilizer from plant B each week.<BR>\n" );
document.write( "the manager wants to make a total of at least 70 tons of fertilizer from both plants each week.\r<BR>\n" );
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document.write( "your constraints are:\r<BR>\n" );
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document.write( "x <= 40<BR>\n" );
document.write( "y <= 50<BR>\n" );
document.write( "x + y >= 70<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "your objective function will be the number of pounds of particulate matter placed into the atmosphere each week.\r<BR>\n" );
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document.write( "plant A places 20 pounds of particulate matter per ton of fertilizer produced.<BR>\n" );
document.write( "plant B places 40 pounds of particulate matter per ton of fertilizer produced.\r<BR>\n" );
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document.write( "your objective function is y = 20x + 40y\r<BR>\n" );
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document.write( "that is the function that you want to minimize.\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would graph the opposite of the constraint functions.\r<BR>\n" );
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document.write( "the are of the graph that is not shaded will be the feasible region.\r<BR>\n" );
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document.write( "you would then evaluate the objective function at each of the corner points of the feasible region to find the minimum amount of particulate placed into the atmosphere.\r<BR>\n" );
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document.write( "my graph looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/101206.jpg\" >\r<BR>\n" );
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document.write( "the evaluation of at the corner points is shown in the following table.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(x,y)               20x + 40y\r\n" );
document.write( "(20,50)             2400\r\n" );
document.write( "(40,50)             2800\r\n" );
document.write( "(40,30)             2000\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "the minimum pounds of particulate placed into the atmosphere is when plant A produces 40 tons of fertilizer and when plant B produces 30 tons of fertilizer each week.\r<BR>\n" );
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document.write( "the constraints for the minimum particulate solution have to be satisfied as well.<BR>\n" );
document.write( "x <= 40 is satisfied because x = 40.<BR>\n" );
document.write( "y <= 50 is satisfied because y = 30<BR>\n" );
document.write( "x + y >= 70 is satisfied because x + y = 70<BR>\n" );
document.write( "x >= 0 and y >= 0 are both satisfied because x and y are both > 0.\r<BR>\n" );
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document.write( "the desmos.com calculator can be found at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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