Answer
The answer is
At $(3,2)=13$
At $(4,10)=32$
At $(5,12)=39$
At $(7,4)=29$
At $(8,6)=36$
Maximum value $=39$.
Minimum value $=13 $.
Work Step by Step
The given objective function is $z=3x+2y $.
The value of the function at each corner points of the graph is shown below.
At $ (3,2) $ is
$z=3(3)+2(2) $
$z=9+4 $
$z=13$.
At $ (4,10) $ is
$z=3(4)+2(10) $
$z=12+20 $
$z=32$.
At $ (5,12) $ is
$z=3(5)+2(12) $
$z=15+24 $
$z=39$.
At $ (7,4) $ is
$z=3(7)+2(4) $
$z=21+8 $
$z=29$.
At $ (8,6) $ is
$z=3(8)+2(6) $
$z=24+12 $
$z=36$.
The maximum value of the objective function is $39$.
The minimum value of the objective function is $13$.
