Question $5$

$(20$ points$)$ Consider the following linear programming problem:

Consider $x_4$ and $x_{5}as$ the slack variables corresponding $to$ the first and second constraints, respec$-$

tively. The final set $of$ equations provided $by$ the simplex tableau $is$:

Conduct $sensitivity$ analysis $by$ independently investigating each $of$ the following changes $in$ the orig$-$

inal model. For each change, use the $sensitivity$ analysis procedure $to$ revise this set $of$ equations $(in$

tableau form$).$

$a.(5$ points$)$ Find the allowable range $to$ stay feasible for the right$-$hand side $of$ the first constraint.

$b.(5$ points$)$ Find the allowable range $to$ stay optimal for the objective coefficient $of{x}_3.$

$c.(10$ points$)$ Introduce a new variable $x_6$ with coefficients:

$\left[\begin{array}{c}{c}_6\\ a_{16}\\ a_{26}\end{array}\right]-\left[\begin{array}{c}-2\\ 2\\ 3\end{array}\right]$

$Is$ the current basis still optimal?