Suppose I've a linear programming problem:

Maximize $2x_1 +x_2 - x_3$ s.t

$ x_1 +2x_2 +x_3 \leq 8 $

$ -x_1 +x_2 -2x_3 \leq 4 $

$ x_1,x_2,x_2 \geq 0 $

and a final tableau:

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What would happen to the optimal solution if I changed the coefficient of $x_2$ in the objective function from $1$ to $5$.

I know decreasing it wouldn't make a difference but not sure how to do sensitivity analysis on this because it is increased and is a non-basic variable..

Also, suppose the coefficient of $x_3$ in the second constraint is changed from $-2$ to $1$. How might this affect the solution?

Could you explain your thought process.. I can only seem to take a high-level guess.


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