Consider the following problem Maximize 2-3x, * *.2% subject to * - *, + 2x, 520 2x, * * - * 510 and Let x, and x denote the stack variables for the respective constraints. After we apply the simplex method the final tableau is Coeffidentot Side Basic Variable EQ Z X 100 3 0 0 B 1 Z (0) 1 0 0 1 1 2 0 * X 1 (2) 0 5 or, after applying revise simplex, the final table is Basic Variable Rhs 30 5 40 X 3 100 f Home Prisen (a) What is the optimal solution to the problem above (all variables)? (2 marks) (b) What is the optimal solution value? (2 marks) Fix x, = 0 in the previous problem to get 2-dimensional problem f= x + 2x = c y + Cuts -X2 + 2x, s 20 = 11 *2* 10 = 62 (C) Perform sensitivity analysis to find the allowable range for C, to stay optimal (d) Perform sensitivity analysis to find the allowable range to stay optimal forcy (e) Perform sensitivity analysis to find the allowable range to stay optimal for by (1) Perform sensitivity analysis to find the allowable range to stay optimal for by (4 marks) 14 marks) (4 marks) (4 marks) Paragraph E Path:p (a) What is the optimal solution to the problem above all s variables)? (2 marks) (b) What is the optimal solution value? (2 marks) Fix X, = 0 in the previous problem to get 2-dimensional problem f = x + 2x = CX + 7 - X + 2x, 5 20 = 1 * * 5 10 = 62 (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 forcy (e) Perform sensitivity analysis to find the allowable range to stay optimal for by (1) Perform sensitivity analysis to find the allowable range to stay optimal for by (4 marks) (4 marks) (4 marks) (4 marks)