document.write( "Question 947643: Find the maximum and minimum of
\n" ); document.write( " z=11x+22y subject to x>=0, y>=0, 4x+5y<=30, 4x+3y<=20, x<=5, y<=8 \n" ); document.write( "

Algebra.Com's Answer #578492 by Fombitz(32388) $\"\"$ $\"About$

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First find the feasible region.
\n" ); document.write( " $\"4x%2B5y=30\"$
\n" ); document.write( " $\"5y=-4x%2B30\"$
\n" ); document.write( " $\"y=-%284%2F5%29x%2B6\"$
\n" ); document.write( " $\"graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C-%284%2F5%29x%2B6%29\"$
\n" ); document.write( " $\"4x%2B3y=20\"$
\n" ); document.write( " $\"3y=-4x%2B20\"$
\n" ); document.write( " $\"y=-%284%2F3%29x%2B20%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C-%284%2F5%29x%2B6%2C-%284%2F3%29x%2B20%2F3%29\"$
\n" ); document.write( "Find the intersection point by substituting,
\n" ); document.write( " $\"%2830-5y%29%2B3y=20\"$
\n" ); document.write( " $\"-2y=-10\"$
\n" ); document.write( " $\"y=5\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"4x%2B3%285%29=20\"$
\n" ); document.write( " $\"4x=5\"$
\n" ); document.write( " $\"x=5%2F4\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "So then the feasible region is,
\n" ); document.write( "

\n" ); document.write( "So the extrema occur at these vertices.
\n" ); document.write( "(0,0): $\"Z=11x%2B22y=11%280%29%2B22%280%29=0\"$
\n" ); document.write( "(0,6): $\"Z=11x%2B22y=11%280%29%2B22%286%29=132\"$
\n" ); document.write( "(5/4,5): $\"Z=11x%2B22y=11%285%2F4%29%2B22%285%29=55%2F4%2B440%2F4=495%2F4\"$
\n" ); document.write( "(5,0): $\"Z=11x%2B22y=11%285%29%2B22%280%29=55\"$ \n" ); document.write( "

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