document.write( "Question 923166: Solve the equation:
\n" ); document.write( "Z = 4x + y
\n" ); document.write( "knowing that:
\n" ); document.write( "x + 2y <= 40
\n" ); document.write( "x + y <= 30
\n" ); document.write( "2x + 3y <= 66\r
\n" ); document.write( "\n" ); document.write( "both x and y are >= 0
\n" ); document.write( "

Algebra.Com's Answer #559893 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
\"x%2B2y%3C=40\"
\n" ); document.write( "\"2y%3C=-x%2B40\"
\n" ); document.write( "\"y%3C=-x%2F2%2B20\"
\n" ); document.write( "Graph \"y=-x%2F2%2B20\"
\n" ); document.write( "\"graph%28300%2C300%2C-10%2C40%2C-10%2C40%2C-x%2F2%2B20%29\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "\"x%2By%3C=30\"
\n" ); document.write( "\"y%3C=-x%2B30\"
\n" ); document.write( "Graph \"y=-x%2B30\" also.
\n" ); document.write( "\"graph%28300%2C300%2C-10%2C40%2C-10%2C40%2C-x%2F2%2B20%2C-x%2B30%29\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "\"2x%2B3y%3C=66\"
\n" ); document.write( "\"3y%3C=-2x%2B66\"
\n" ); document.write( "\"y%3C=-%282%2F3%29x%2B22\"
\n" ); document.write( "Graph \"y=-%282%2F3%29x%2B22\" also.
\n" ); document.write( "\"graph%28300%2C300%2C-10%2C40%2C-10%2C40%2C-x%2F2%2B20%2C-x%2B30%2C-%282%2F3%29x%2B22%29\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Find the points of intersection.
\n" ); document.write( "\"-x%2F2%2B20=-%282%2F3%29x%2B22\"
\n" ); document.write( "\"%28-1%2F2%2B2%2F3%29x=2\"
\n" ); document.write( "\"%281%2F6%29x=2\"
\n" ); document.write( "\"x=12\"
\n" ); document.write( "Then,
\n" ); document.write( "\"y=-12%2F2%2B20=-6%2B20=14\"
\n" ); document.write( "(12,14)
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".\r
\n" ); document.write( "\n" ); document.write( "\"-x%2B30=-%282%2F3%29x%2B22\"
\n" ); document.write( "\"-%281%2F3%29x=-8\"
\n" ); document.write( "\"x=24\"
\n" ); document.write( "Then,
\n" ); document.write( "\"y=-24%2B30=6\"
\n" ); document.write( "(24,6)
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "The extrema of Z occur at one of these vertices.
\n" ); document.write( "Not sure if you need the maximum or minimum.
\n" ); document.write( "(0,0) : \"4x%2By=4%280%29%2B0=0\"<-- Minimum
\n" ); document.write( "(0,20) :\"4x%2By=4%280%29%2B20=20\"
\n" ); document.write( "(12,14) :\"4x%2By=4%2812%29%2B14=62\"
\n" ); document.write( "(24,6) :\"4x%2By=4%2824%29%2B6=102\"
\n" ); document.write( "(30,0) : \"4x%2By=4%2830%29%2B0=120\"<-- Maximum
\n" ); document.write( "
\n" );