Question 1023175
Solution by the graphical method.  (Typesetting here of simplex method would be brutal.  The graphical method is a little less difficult, but the region of feasibility will not be reproduced.)

The region of feasibility would be a hexagon (six-sided) figure with the following corner points (in ccw direction):
(0,0), (20,0), (20,6), (21/2,69/2), (5,40), and (0,40).
For (0,0), Z = 0
For (20,0), Z = 8*20 = 160
For (20,6), Z = 202
For (21/2,69/2), Z = 325.5
For (5,40), Z = 320, and 
For (0,40), Z = 280
By the fundamental theory of linear programming the maximum exists at the point (21/2,69/2) with a Z value of 325.5.