Given some function $f = x + 2y + 3z$ on the set which is defined as:
$\begin{cases} x \geq 0\\ y \geq 0\\ x + y \leq 3\\ x + y \leq z\\ 3x + 3y \geq z \end{cases}$
As I understood, such restriction represents the area between two planes and there is a some figure that moves up and down intersecting the area.
My depicting skills are bad and neither I can apply Lagrange multipliers or any other technique here.
So how do I find the minimum and maximum value of $f$?
i have found that $$f(x,y,z)\le 33$$ and the equal sign holds for $$x=0,y=3,z=9$$