Maximize z=4x+2y subject to:
x-y<10
5x+3y<75
x+y<20
X>0
y>0
make a sketch and shade in the region.
(I used the intercepts of the corresponding equations to draw the lines)
I got a region with critical points of (13.125, 3.125) and (7.5, 12.5) inside the first quadrant after solving the simple equations.
Slide the line 4x + 2y = z parallel to itself until you reach the farthest point of the region.
I found that to be (13.125, 3.125)
so z = 4(13.125) + 2(3.125) = 58.75