Consider the following linear programming problem

$$\begin{array}{ll} \text { maximise } & -2 x_{1}+3 x_{2} \\ \text { subject to } & x_{1}-x_{2} \geq 1 \\ & 4 x_{1}-x_{2} \geq 10 \\ & x_{2} \leq 6 \\ & x_{i} \geq 0, i=1,2 \end{array}$$

Write down the Phase One problem for (1) and solve it.

By using the solution of the Phase One problem as an initial basic feasible solution for the Phase Two simplex algorithm, solve (1), i.e., find the optimal tableau and read the optimal solution $\left(x_{1}, x_{2}\right)$ and optimal value from it.