Question about sensitivity analysis of an LP problem. Range for the dual be unfeasible.

Question

Let an LP of the form:

$\max \ ax_1+x_2$

$s.t. \ -x_1+x_2 \leq 3$

$\ -bx_1+x_2\leq6$

$\ \ \ \ \ \ \ \ x_1,x_2\geq0$

For which range of values of $a$ and $b$ we have an unfeasible dual problem?

I know that the primal problem should be unbounded in order to the dual problem be unfeasible, but I dont know how to go any further.

Answer 1

Hint:

Let's write down the dual:

$$\min 3p_1 + 6p_2$$

$$-p_1-bp_2 \geq a$$

$$p_1+p_2 \geq 1$$

$$p_1, p_2 \geq 0$$

This is a $2$ dimensional problem, draw out the domain of dual and check if it is feasible.