operations research

Consider the following LP problem. Maximize 2-3x + xy + 2x subject to * - *x + 2x, 20 2x + xy - x, 10 and X, 20, X220, *, 20. Let *4 and x denote the slack variables for the respective constraints. After we apply the simplex method, the final simplex tableau is Coefficient of: Basic Right Variable Eq. Z X X Side X X4 Z (0) 8 0 0 3 4 100 X 1 (1) 0 3 0 1 1 1 30 x X (2) 0 5 1 0 1 2 40 or, after applying revise simplex, the final table is Basic Variable Rhs -X, 30 3 X 40 5 2 or, after applying revise simplex, the final table is Basic Variable Rhs -X, -X5 X 30 3 1 1 X2 40 5 2 100 00 3 4 (a) What is the optimal solution to the problem above (all 5 variables)? (2 marks) (b) What is the optimal solution value? (2 marks) Fixx, = 0 in the previous problem to get 2-dimensional problem f=x + 2x3 = CX2 + cxz -X2 + 2x3 = 20 = b1 * - *3 5 10 = b2 (c) Perform sensitivity analysis to find the allowable range for cz to stay optimal (d) Perform sensitivity analysis to find the allowable range to stay optimal for cz (e) Perform sensitivity analysis to find the allowable range to stay optimal for by (f) Perform sensitivity analysis to find the allowable range to stay optimal for by