Consider the following problem.

Maximize Z 2x1  x2  x3, subject to 3x1  x2  x3 60 x1  x2  2x3 10 x1  x2  x3 20 and x1  0, x2  0, x3  0.

Let x4, x5, and x6 denote the slack variables for the respective constraints. After we apply the simplex method, the final simplex tableau is Now you are to conduct sensitivity analysis by independently investigating each of the following six changes in the original model.
For each change, use the sensitivity analysis procedure to revise this final tableau and convert it to proper form from Gaussian elimination for identifying and evaluating the current basic solution.
Then test this solution for feasibility and for optimality. If either test fails, reoptimize to find a new optimal solution.

(a) Change the right-hand sides from to .

(b) Change the coefficients of x1 from to .

(c) Change the coefficients of x3 from to .

(d) Change the objective function to Z 3x1  2x2  3x3.

(e) Introduce a new constraint 3x1  2x2  x3 30. (Denote its slack variable by x7.)

(f) Introduce a new variable x8 with coefficients .
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