Consider the region given by

$x7,$

$x+y9,$

$2x-2y-z5,$

$x,y,z0$

$($a$)$ Formulate the problem using slack variables $s_{1}0,s_{2}0$ and $s_{3}0.$ Write down the basic solution obtained by choosing the slack variables as

pivots. Enter in the form $(x,y,z,s_1,s_2,s_3).$

$($b$)$ Is this a feasible solution?

True

False

$($c$)$ Write down the basic solution obtained by choosing $z,s_1,s_2$ as pivots. Enter in the form $(x,y,z,s_1,s_2,s_3)$

$($d$)$ Is this a feasible solution?

True

False

$($e$)$ Write down the basic solution obtained by choosing $x,y,z$ as pivots. Enter in the form $(x,y,z,s_1,s_2,s_3)$

$($f$)$ Is this a feasible solution?

True

False