The best advice that we can give you is to solve by graphing:

5x + 8 >=200

25x -10y>=150

x+y<=150

x>=0 , y>=0

The optimal feasible solution are achieved at the points of intersection.

Click here to see the graph:

The intersection points are:

(38.4, 81), (47.14, 102.86), (150, 0) and (38.4, 0)

Now we calculate z for each of the above points:

z=10*38.4+20*81 = 2004

z=10*47.14+20*102.86 = 2528.6

z=10*150+20*0 = 1500

z=10*38.4+20*0 = 384

The function z=10x+20y is maximized at the point (47.14, 102.86).