2. Consider the following parametric linear programming problem, where the parameter 8 must be nonnegative: Maximize...

 

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2. Consider the following parametric linear programming problem, where the parameter 8 must be nonnegative: Maximize Z(0)=(5+20)x+(2-0) x +(3+0) X3, subject to 4x1+x2 25+50 3x1 + x2 + 2x3 = 10-100 x 0, X2 0, X3 0. Let x4 be the surplus variable for the first functional constraint, and let s and 6 be the artificial variables for the respective functional constraints. After we apply the simplex method with the Big M method and with 0=0, the final simplex tableau is Basic Variable Z X2 X4 Eq. Z (0) 1 (1) (2) 0 XI 1 3 -1 X2 0 1 0 Coefficient of: X3 1 2 2 X4 0 10 1 MRI XS 0 -1 x6 M+2 1 Right Side 20 10 5 (a) Use the fundamental insight to revise this tableau to reflect the inclusion of the parameter in the original model. Show the complete tableau needed to apply the feasibility test and the optimality test for any value of Express the corresponding basic solution (and Z) as a function of 0. (10%) 5) Determine the range of nonnegative values of 0 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%) 2. Consider the following parametric linear programming problem, where the parameter 8 must be nonnegative: Maximize Z(0)=(5+20)x+(2-0) x +(3+0) X3, subject to 4x1+x2 25+50 3x1 + x2 + 2x3 = 10-100 x 0, X2 0, X3 0. Let x4 be the surplus variable for the first functional constraint, and let s and 6 be the artificial variables for the respective functional constraints. After we apply the simplex method with the Big M method and with 0=0, the final simplex tableau is Basic Variable Z X2 X4 Eq. Z (0) 1 (1) (2) 0 XI 1 3 -1 X2 0 1 0 Coefficient of: X3 1 2 2 X4 0 10 1 MRI XS 0 -1 x6 M+2 1 Right Side 20 10 5 (a) Use the fundamental insight to revise this tableau to reflect the inclusion of the parameter in the original model. Show the complete tableau needed to apply the feasibility test and the optimality test for any value of Express the corresponding basic solution (and Z) as a function of 0. (10%) 5) Determine the range of nonnegative values of 0 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%)