Consider the following problem.

Maximize Z 2x1  x2  x3, subject to 3x1  2x2  2x3 15

x1  x2  x3 3 x1  x2  x3 4 and x1  0, x2  0, x3  0.

If we let x4, x5, and x6 be the slack variables for the respective constraints, the simplex method yields the following final set of equations:

(0) Z  2x3  x4  x5 18,

(1) x2  5x3  x4  3x5 24,

(2) 2x3  x5  x6 7,

(3) x1  4x3  x4  2x5 21.

Now you are to conduct sensitivity analysis by independently investigating each of the following eight 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 coefficient of x3 in the objective function to c3 2.

(c) Change the coefficient of x1 in the objective function to c1 3.

(d) Change the coefficients of x3 to

.

(e) Change the coefficients of x1 and x2 to and , respectively.

(f) Change the objective function to Z 5x1  x2  3x3.

(g) Change constraint 1 to 2x1  x2  4x3 12.

(h) Introduce a new constraint 2x1  x2  3x3 60.