document.write( "Question 176608: graph each system of constraints. find all vertices. evaluate the objective function at each vertex to find teh maximum or minimum value..:)\r
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\n" ); document.write( "\n" ); document.write( "1)x<3
\n" ); document.write( " y<7
\n" ); document.write( " x>0,y>0
\n" ); document.write( "maximum for p=2x+3y\r
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\n" ); document.write( "\n" ); document.write( "2) 2x+y<30
\n" ); document.write( " x+y<20
\n" ); document.write( " x>0, y>0
\n" ); document.write( "minimum for c=x+4y\r
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Algebra.Com's Answer #131686 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
1)\"0+%3C=++x+%3C=+3\"
\n" ); document.write( "\"0+%3C=+y+%3C=+7\"
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\n" ); document.write( "\"P%28x%2Cy%29=2x%2B3y\"
\n" ); document.write( "\"P%280%2C0%29=2%280%29%2B3%280%29=0\"
\n" ); document.write( "\"P%283%2C0%29=2%283%29%2B3%280%29=6\"
\n" ); document.write( "\"P%283%2C7%29=2%283%29%2B3%287%29=27\"
\n" ); document.write( "\"P%280%2C7%29=2%280%29%2B3%287%29=21\"
\n" ); document.write( "Max. value=27 occuring at (3,7), min. value =0 occuring at (0,0).
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\n" ); document.write( "2)First find the feasible region bounded by the lines,
\n" ); document.write( "\"2x%2By%3C=30\"
\n" ); document.write( "\"y%3C=30-2x\"
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\n" ); document.write( "\"x%2By%3C=20\"
\n" ); document.write( "\"y%3C=20-x\"
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\n" ); document.write( "\"x%3E=0\"
\n" ); document.write( "\"y%3E=0\"
\n" ); document.write( "Let's look at the graph of the two lines.
\n" ); document.write( "The vertices are then the x-intercept and y-intercept of the graphs.
\n" ); document.write( " \"+graph%28+300%2C+300%2C+-2%2C+18%2C+-2%2C+38%2C+20-x%2C+30-2x%29+\"
\n" ); document.write( "Y-intercept: (0,20)
\n" ); document.write( "X-intercept: (15,0)
\n" ); document.write( "The final point is their intersection point.
\n" ); document.write( "\"30-2x=20-x\"
\n" ); document.write( "\"x=10\"
\n" ); document.write( "\"y=10\"
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\n" ); document.write( "\"C%28x%2Cy%29=x%2B4y\"
\n" ); document.write( "\"C%280%2C0%29=0%2B4%280%29=0\"
\n" ); document.write( "\"C%2815%2C0%29=15%2B4%280%29=15\"
\n" ); document.write( "\"C%2810%2C10%29=10%2B4%2810%29=50\"
\n" ); document.write( "\"C%280%2C20%29=0%2B4%2820%29=80\"
\n" ); document.write( "The minimum for C=x+4y is 0 and occurs at (0,0).
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