Post-optimality analysis: Change in one of the constraints

1. The problem statement, all variables and given/known data



Consider the LP:



max [itex]\, -3x_1-x_2[/itex]

[itex]\,\,[/itex]s.t. [itex]\,\,\,\,[/itex] [itex]2x_1+x_2 \leq 3[/itex]

[itex]\quad \quad \ -x_1+x_2 \geq 1[/itex]

[itex]\quad \quad \quad \quad \ x_1,x_2 \geq 0[/itex]





Suppose I have solved the above problem for the optimal solution. (I used dual simplex and get (0,1) as the optimal solution.)

Now if the first constraint [itex](2x_1+x_2 \leq 3)[/itex] is either changed to



(1) max [itex]\, (2x_1+x_2,0) \leq 3[/itex], or

(2) max [itex]\, (2x_1+x_2,6)\leq 3[/itex],



is it possible to obtain the new optimal solution without having to solve the entire problem from the scratch?







2. Relevant equations







3. The attempt at a solution





I have tried introducing a new variable t to address the maximum and rewrite the constraints in linear form but it doesn't seem to help.



Any hint or comment is greatly appreciated, thank you!