Question 323823
First find the feasible region using the constraints.
Find the intersection points.
{{{9-x=5+x}}}
{{{2x=4}}}
{{{x=2}}}
{{{y=7}}}
(2,7)
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{{{9-x=2x+14}}}
{{{3x=-5}}}
{{{x=-5/3}}}
{{{y=9-(-5/3)=32/3}}}
(-5/3,32/3)
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{{{2x+14=5+x}}}
{{{x=-9}}}
{{{y=5-9=-4}}}
(-9,-4)
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{{{drawing(300,300,-10,10,-5,15,grid(1), circle(-9,-4,.4),circle(-5/3,32/3,0.4),circle(2,7,0.4),graph(300,300,-10,10,-5,15,9-x,5+x,2x+14))}}}
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The min and max of the function will occur at one of the vertices:
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(2,7):{{{z=2x+3y=2(2)+3(7)=25}}}
(-5/3,32/3):{{{z=2x+3y=2(-5/3)+3(32/3)=86/3}}}
(-9,-4):{{{z=2x+3y=2(-9)+3(-4)=-30}}}
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The min value of z of -30 occurs at (-9,-4).
The max value of z of 86/3 occurs at (-5/3,32/3).