[6.54] Consider the following linear programming problem and its optimal final tableau shown below: Maximize2x1+x2x3subjecttox1+2x2+x38 Final Tableau: a. Write the dual problem and give the optimal dual variable values 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: x2+ 2x3=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? f. Suppose that a new activity x6 is proposed with unit return 6 and consumption vector a6=(2,1)t. Find a new optimal solution