Answer
The answer is
at $(1,2)=17$
at $(2,10)=70 $
at $ (7,5) =65$
at $ (8,3) =58 $
Maximum $ =70 $ and Minimum $=17 $
Work Step by Step
The given objective function is $ z=5x+6y $.
The value of the function at each corner points of the graph is shown below.
At $(1,2) $
$ z=5(1)+6(2) $
$ z=5+12 $
$ z=17 $.
At $(2,10) $
$ z=5(2)+6(10) $
$ z=10+60 $
$ z=70 $.
At $(7,5) $
$ z=5(7)+6(5) $
$ z=35+30 $
$ z=65 $.
At $(8,3) $
$ z=5(8)+6(3) $
$ z=40+18 $
$ z=58 $.
The maximum value of the objective function is $ 70 $.
The minimum value of the objective function is $17 $.
