Consider the following problem.

Maximize Z 2x1  7x2  3x3, subject to x1  3x2  4x3 30 x1  4x2  x3 10 and x1  0, x2  0, x3  0.

By letting x4 and x5 be the slack variables for the respective constraints, the simplex method yields the following final set of equations:

(0) Z  x2  x3  2x5 20,

(1)  x2  5x3  x4  x5 20,

(2) x1  4x2  x3  x5 10.

Now you are to conduct sensitivity analysis by independently investigating each of the following seven changes in the original model. For each change, use the sensitivity analysis procedure to revise this set of equations (in tableau form) 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 to  .

(b) Change the coefficients of x3 to .

(c) Change the coefficients of x1 to .

(d) Introduce a new variable x6 with coefficients .

(e) Change the objective function to Z x1  5x2  2x3.

(f) Introduce a new constraint 3x1  2x2  3x3 25.
(g) Change constraint 2 to x1  2x2  2x3 35.