What shape is the feasible set x y z 20 x y z greaterthan

What shape is the feasible set {x + y + z = 20 x, y, z greaterthanorequalto 0 and what is the maximum of x + 2y + 3z?

The eqn x+y+z =1 represents eqn of a plane passing trough te points (1,0,0) , (0,1,0) and (0,0,1)

as x,y,z>0 t these intersecting points will give max value for x+2y+3z

at (1,0,0) value of x+2y+3z = 1

at (0,1,0) value of x+2y+3z = 2 and

at (0,0,1) value of x+2y+3z=3

max of x+2y+3z is 3 attained at (0,0,1)