Question 117459
The constraints marks the feasible region that lies on and within this green lined polygon.

{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),

circle( 0, 0, .2 ),
circle( 0, 1, .2 ),
circle( 4, 0, .2 ),
circle( 4, 3, .2 ),
green(line(0,0,0,1)),
green(line(0,1,4,3)),
green(line(4,3,4,0)),
green(line(4,0,0,0))
)}}}
From linear programming, a solution exists at one of the bounding vertices (0,0), (0,1), (4,0), or (4,3). 
A=20x+30y 
A(0,0) = 20(0)+ 30(0)= 0
A(0,1) = 20(0)+ 30(1) = 30
A(4,0) = 20(4)+ 30(0) = 80
A(4,3) = 20(4)+ 30(3) = 170
The (x,y) pair that maximizes A in the feasible region is (4,3).