Question: X1, X2, X3 are nonnegative variables Given the solved final simplex tableau: Coefficient of: Basic Variables RHS X1 X2 X3 s1 s2 z 2 2/3

X1, X2, X3 are nonnegative variables Given the

X1, X2, X3 are nonnegative variables Given the solved final simplex tableau: Coefficient of: Basic Variables RHS X1 X2 X3 s1 s2 z 2 2/3 1 1/3 0 0 2 1/3 25 2/3 s1 1/3 1 2/3 0 1 - 1/3 5 1/3 X3 1 2/3 1 1/3 0 1/3 3 2/3 (Note: The number is in mixed number form) a. Show your algebraic steps to find the allowable range of the right-hand side values b in the objective function so that the current optimal solution does not change. (30pts) b. Now, supposed that in the final tableau, the increase amount Ac in term of 8 for each coefficient of variable in row 0 is as follow: Ac = [0 20 0 0 - 0 ] For 020, give the range of value of 0 for which this solution is both feasible and optimal. Use this tableau to identify the current basic solution as a function of e. What is the best choice of 0 within this range? (20pts) X1, X2, X3 are nonnegative variables Given the solved final simplex tableau: Coefficient of: Basic Variables RHS X1 X2 X3 s1 s2 z 2 2/3 1 1/3 0 0 2 1/3 25 2/3 s1 1/3 1 2/3 0 1 - 1/3 5 1/3 X3 1 2/3 1 1/3 0 1/3 3 2/3 (Note: The number is in mixed number form) a. Show your algebraic steps to find the allowable range of the right-hand side values b in the objective function so that the current optimal solution does not change. (30pts) b. Now, supposed that in the final tableau, the increase amount Ac in term of 8 for each coefficient of variable in row 0 is as follow: Ac = [0 20 0 0 - 0 ] For 020, give the range of value of 0 for which this solution is both feasible and optimal. Use this tableau to identify the current basic solution as a function of e. What is the best choice of 0 within this range? (20pts)

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