please help to find the maximum and minimum of the objective function.

Hello, please help me to find the maximum and minimum of the following objective function (if they do exist) if there's no maximum state the reason.

f =3x+4y

then I'm given a graph with these points

(0,6)

(1,3)

(2,1)

(4,0)

thank you.

I would say the maximum is 24 at the points (0,6) however, that's wrong, according to my textbook, there's no maximum, why????

concerning the minimum, I agree with my textbook, the minimum is 10 at the points (2,1)

thank you.