Question 5: Consider the following problem. Maximize Z-5X, + 5X₂+ 13X, subject to -X₁ + X₂+ 3X, ≤20 (constraint 1) 12X, + 4x2 + 10X390 (constraint 2) X₁≥ 0, X,≥0, X,≥0 The optimal table for the problem is as follows: X₁ X₂ X3 S₁ S₂ RHS Z 0 0 2 5 0 100 -1 X2 1 3 1 0 20 16 S₂ 0 -2 -4 1 10 Now you are to conduct sensitivity analysis by independently investigating each of the following nine changes in the original model. Explain what happens and how the optimal table changes according to the change. Test the new solution for feasibility and optimality. If optimality is violated as a result of change, do not re-optimize. (a) Change the right-hand side of constraint 1 to b₁ = 30. (b) Change the right-hand side of constraint 2 to b₂ = 70. (c) Change the right-hand sides to (d) Change the coefficient of X, in the objective function to 8. (e) Change the coefficient of X, in the objective function to -2, change the coefficient of X₁ in the first constraint to 0 and change the coefficient of X, in the second constraint to 5. Suppose all these three changes are conducted simultaneously. (f) Change the coefficient of X2 in the objective function to 6, change the coefficient of X2 in the first constraint to 2 and change the coefficient of X, in the second constraint to 5. Suppose all these three changes are conducted simultaneously. (g) Introduce a new variable X, whose objective function coefficient is 10, coefficient in the first constraint is 3 and coefficient in the second constraint is 5. (h) Introduce a new constraint: 2X, + 3X2 + 5X, ≤ 50 (i) Change constraint 2 to: 10X, +5X2 + 10X3≤ 100