# How to find range of values for the first-stage decisions resulting in the same cuts in two-stage stochastic programming?

Suppose we have a two-stage stochastic program as follows: $$$$\begin{split} \min \ & c^Tx + \mathbb{E}_\xi[Q(x,\xi)] \\ & \text{where}\\ &Q(x,\xi)=\min q(\xi)^Ty\\ &Tx+W(\xi)y=h(\xi)\\ &y \ge 0 \end{split}$$$$ I am wondering how it is possible to find a set of values for the first-stage decisions such that in the L-Shape method, the same (optimality) cuts are generated. For example, suppose we have a problem like the follows:

$$$$\begin{split} \min \ & 5x_1+10x_2 + \mathbb{E}_\xi[q_1y_1+q_2y_2] \\ & y_1 + 2y_2 \ge d_1 -x_1 \\ & y_1 \ge d_2 -2x_2\\ & 0 \le x_1 \le 10 \\ & 0 \le x_2\le 10 \\ & y_1,y_2 \ge 0 \end{split}$$$$

where $$(q_1,q_2,d_1,d_2)$$ takes two values $$(20,10,5,10)$$ and $$(15,25,12,5)$$ with equal probabilities.