Problem 2 Consider the following problem: Maximize Z = -5x₁ +5x2 + 13x3 subject to -x1 + x2 + 3x3 ≤ 20 12x1 + 4x2 +10x3 ≤ 90 and x; ≥ 0 for j = 1,2,3. The simplex method yields the following final simplex table: Cj -5 5 13 0 0 xi Ci x1 X2 X3 x4 X5 bi X2 X5 5 -1 1 3 1 0 20 0 16 0 -2 -4 1 10 Zj -5 5 15 5 0 100 Cj - Zj 0 0 -2 -5 0 Now you are to conduct the sensitivity analysis by independently investigating each of the following nine changes in the original model. For each change, use the sensitivity analysis procedure to revise this table and convert it to the proper form for identifying and evaluating the current basic solution. Then test this solution for feasibility and for optimality. (Do not reoptimize.) 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 of constraints 1 and 2 to b₁ = 10; b₂ = 100. d) Change the coefficient of x3 in the objective function to c3 = 8. e) Change the coefficients of x₁ to c₁ = -2; a₁₁ = 0; a21 = 5. f) Change the coefficients of x2 to c₂ = 6; α12 = 2; a22 = 5. g) Introduce a new variable x with coefficients C6 = 10; α16 = 3; a26 = 5. h) Introduce a new constraint 2x₁1 + 3x2 + 5x3 ≤ 50. (Denote its slack variable by x6). i) Change constraint 2 to 10x₁ + 5x2 + 10x3 ≤ 100.