$($a$)$ Show that directions $$ z$112=12,02$ and

$$ z$122=1-2,42$ are improving directions for this model at every z$.$

$($b$)$ Beginning at z$102=10,02,$ execute Improving Search Algorithm $3$A on the

model. Limit your search to the two directions of part $($a$),$ and continue until

neither is both improving and feasible.

$($c$)$ Show in a two$-$dimensional plot the feasible space and objective function contours

of the model. Then plot the path of your

search in part $($b$).$