B$.$ Changes that affect OPTIMALITY:

Changing the Z $-$coefficient

Changing the left$-$hand$-$side $($LHS$)$ coefficient of a non$-$basic variable

Adding a new variable

Example B: Consider the following LP:

$]10[0$

Optimal tableau $($using generalized simplex method$)$:

$\backslash$table$[[$BV$,x_1,x_2,s_1,s_2,$RHS$],[z,0,2,6,0,60],[s_2,0,1,2,1,16],[x_1,1,1,1,0,10]]$

Find how does each of the following scenarios affect the current optimal $($and feasible$)$ solution:

vedued $cos+f{x}_1=10y_1-4y_2-2$

a$.$ Change the value of $c_1$ to be $2.$

$($Answer: the current solution becomes not optimal, new $z=40)$

b$.$ Change the value of $a_{12}$ to be $0\mathrm{.}5($coefficient of $x_2$ in constraint$1).$

$($Answer: the current solution becomes not optimal, new $z=80)$

c$.$ Add a new variable $x_3$:$c_3=3,a_{13}=-2,a_{23}=5$

$($Answer: the current solution becomes not optimal, new $z=300)$