Question $3$

Consider the following linear programming $($LP$)$ problem.

Maximize $z=-x_1+3x_2+6x_3$

$-x_1+x_2+3x_{3}20$

$3x_1+2x_2+5x_{3}45$

$x_1,x_2,x_{3}0$

We introduce two slack variables $x_4$ and $x_5$ for the respective constraints. The optimal

tableau is given in Table Q$3$ below.

Table $03$

We implement sensitivity analysis for each of the following changes with regard to the

original model.

$($a$)$ When the value of $b_1$ changes from $20$ to $25,$ find the modified tableau.

Subsequently solve the new LP problem.

$(7$ marks$)$