Question 1202520
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Plot the five inequalities shown using graphing software such as Desmos or GeoGebra. 
The overlapped shaded region is a quadrilateral with these five corner points
(0,0)
(0,2)
(1,3)
(3,1)
(3,0)


Test each corner point with the objective function to see which gives the largest value of z.


Testing (0,0)
z=4x+5y
z=4*0+5*0
z=0


Now try (0,2)
z=4x+5y
z=4*0+5*2
z=10
This result is larger than the previous.
So far (0,2) yields the largest z value.


Now try (1,3)
z=4x+5y
z=4*1+5*3
z=19
This result is larger than the previous.


Now try (3,1)
z=4x+5y
z=4*3+5*1
z=17
This result is NOT larger than the previous. So we ignore this.


Lastly we need to try (3,0)
z=4x+5y
z=4*3+5*0
z=12
This result is NOT larger than 19, so we ignore this.



Answer: 
The max value is z = 19.
It occurs when (x,y) = (1,3)
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