Solve the given linear programming problem graphically Maxim

Solve the given linear programming problem graphically:

Maximize f=2x+y+3z

Subject to: x+2z8

-y+3z10

- x+y-z12

x0 ; y0 ; z0

x = 8, y = 20, z = 0

If you subtract the 3rd equation from the first, 2x - y + 3z <= -4 But -y + 3z <= 10 => x >= 8. But

x + 2z <= 8, so x = 8 and since x,y,z >= 0, z = 0.

-x + y <= 12 gives y = 20

Max = 36