[6.54] Consider the following linear programming problem and its optimal final tableau shown below: Maximize 2x1 + x2 - X3 subject to x + 2x3 + x 38 - x1 + x2 - 2x3 = 4 x1, x2, x > 0. Final Tableau: Z X1 X2 33 1 3 -1 16 8 1 1 0 1 12 b. c. d. from the foregoing tableau. Using sensitivity analysis, find a new optimal solution if the coefficient of x2 in the objective function is changed from 1 to 5. 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. Suppose that the following constraint is added to the problem: x2 + 2x3 = 3. Using sensitivity analysis, find the new optimal solution. 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? Suppose that a new activity x6 is proposed with unit return 6 and consumption vector ag = (2,1)'. Find a new optimal solution. e. f