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

$Q1.$ Consider the following problem, using algebraic $sensitivity$ analysis:

Maximize

Subject $to$

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 $of$ the coefficient $of{x}_1(c_1)$ that keeps the current solution optimal; assuming the coefficient

$of{x}_2(c_2)is$ constant. $(7$ points$)$

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