$[6\mathrm{.}33]$ Consider the following linear programming problem:

Maximize $2x_1-3x_2$

subject $to{x}_1+x_{2}3$

$3x_1+x_{2}6$

$x_1,x_{2}0.$

You are told that the optimal solution is $x_1=\frac{3}{2}$ and $x_2=\frac{3}{2}.$ Verify this

statement by duality. Describe two procedures for modifying the problem in

such a way that the dual simplex method can be used. Use one of these

procedures for solving the problem by the dual simplex method.