Consider the following linear programming problem and its optimal final tableau shown below: Maximum 2x1 + x2- x3
subject to x1 + 2x2 + x3 <= 8
-x1 + x2 - 2x3 <= 4
x1, x2 x3 >=0

Required:
a. Write the dual problem and find the optimal dual variables from the foregoing tableau.
b. Using sensitivity analysis, find a new optimal solution if the coefficient of x2 in the objective function is changed from 1 to 5.
c. Suppose that the coefficient of x2 in the first constraint is changed from +2 to 1/6. Using sensitivity analysis, find a new optimal solution.
d. Suppose that the following constraint is added to the problem: x^2 + 2x^3 = 3. Using sensitivity analysis, find the new optimal solution.
e. If you were to choose between increasing the right-hand-side of the first and second constraints, which one would you choose? Why? What is the effect of this increase on the optimal value of the objective function?