Given the LPP

max,$z=14x_1+20x_2+10x_3$

$s.t.6x_1+10x_2+3x_{3}100$

$,8x_1+10x_2+6x_{3}120$

$,4x_1+8x_2+9x_{3}150$

$,x_1,x_2,x_{3}0$

$($i$)$ Solve by revised simplex method;

$($ii$)$ Find the value of $c_1$ so that $x_1$ contributes in the optimal solution;

$($iii$)$ What is the lower limit for $c_2$ so that $x_2$ remains in the optimal solution?

$($iv$)$ What will be the impact on optimal solution if $b_1$ is changed from $100$ to $103?$ from $100$ to $200?$