$[5\mathrm{.}46]$ Consider the following problem:

Maximize $2x_1+3x_2$

subject $to{x}_1+x_2-8$

$,-2x_1+3x_{2}0$

$,x_1,x_{2}0.$

a$.$ Solve the problem geometrically. Starting at the origin, at each iteration

identify the variable that enters and the variable that leaves the basis.

b$.$ Write the KKT conditions and show that they hold at optimality.