Consider the mathematical program

max,$5x_1+x_2$

$s.t.2x_1+x_{2}6$

$,x_1-x_{2}0$

$,x_1,x_{2}0$

Beginning at $x^{(0)}=(1,1),$ execute Improving Search Algorithm on the model. Limit your search

to two directions, $x^{(1)}=(1,2)$ and $x^{(2)}=(1,-2),$ and continue until neither is both improving

and feasible.