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.