Clarification needed for this linear programming problem

Question

I am stuck on the following problem:

Consider the following optimization problem: $$\text{Maximize }3x+4y+2z\text{ subject to}$$ $$x+y+z\le12$$ $$x+2y-z\le5$$ $$x-y+z\le2$$ $$\text{where } x,y,z \ge 0$$

Then,

1. the problem has more than one feasible solution.
2. the objective function of the dual program is to minimize $12u+5v+2w$
3. one of the constraints of the dual program is $u-v+w\ge2$
4. two of the constraints of the dual program are $u+v+w\le and u+2v-w\le4$

I have got only confusion over option (1). The options (2) and (3) are correct and option (4) is wrong. But how can I check whether the problem has more than one feasible solution? Can someone explain? Thanks and regards.

Answer 1

A feasible solution is an assignment of $x,y,z$ that satisfies the constraints but doesn't have to be optimal.

$x=0,y=0,z=0$ and $x=1,y=1,z=1$ both work.