Solve the following linear programming problem using the simplex method:

$$\begin{array}{r} \max \left(x_{1}+2 x_{2}+x_{3}\right) \\ \text { subject to } \quad x_{1}, x_{2}, x_{3} \geqslant 0 \\ x_{1}+x_{2}+2 x_{3} \leqslant 10 \\ 2 x_{1}+x_{2}+3 x_{3} \leqslant 15 \end{array}$$

Suppose we now subtract $\Delta \in[0,10]$ from the right hand side of the last two constraints. Find the new optimal value.