SENSITIVITY AND POST OPTIMAL ANALYSIS $(50$ points$)$

Q$1.$ Consider the following problem, using algebraic sensitivity analysis:

Maximize $z=2x_1+6x_2$

Subject $to$

$6x_1+4x_{2}24$

$x_1+2x_{2}8$

$x_{2}2$

$x_1,x_{2}0$

Given that the following is optimal tableau:

$($a$)$Classify each one of the three constraints as either binding or abundant and justify your answers. $(3$ points$)$

$($b$)$Compute the range of $c_1$ assuming $c_2$ is constant. $(7$ points$)$

$($c$)$ Compute the unit worth of resource $1($defined by the first constraint$)$ and the range of its validity. $(10$ points$)$