12. Consider the following parametric linear programming problem, where the parameter 6 must be nonnegative: Maximize ZO) = (5 +20)x1+ (2 - 0)x2 + (3 + x3, subject to 4x1 + x2 > 5 + 50 3x1 + x2 + 2x3 = 10 - 100 x120, X220, X30. Let x4 be the surplus variable for the first functional constraint, and let is and I be the artificial variables for the respective functional constraints. After we apply the simplex method with the Big M method and with JO=0, the final simplex tableau is Coefficient of: Basic Variable Eq. 9. 2 X1 X2 X3 X4 s Side (0) 1 0 1 0 M M + 20 (1) 1o 3 1 2 0 0 1 10 | (2) | 0 -1 0 2 1 -1 1 5 a) Use the fundamental insight to revise this tableau to reflect the inclusion of the parameter 0 in the original model. Show the complete tableau needed to apply the feasibility test and the optimality test for any value of 2. Express the corresponding basic solution (and Z) as a function of 0. (10%) 5) Determine the range of nonnegative values of over which this basic solution is feasible. (5%) Determine the range of nonnegative values of over which this basic solution is both feasible and optimal. etermine the best choice of over this range. (5%)