Consider the following problem.

Maximize Z 3x1  5x2  2x3, subject to

2x1  2x2  x3 5

3x1  x2  x3 10 and x1  0, x2  0, x3  0.

Let x4 and x5 be the slack variables for the respective functional constraints. After we apply the simplex method, the final simplex tableau is Parametric linear programming analysis now is to be applied simultaneously to the objective function and right-hand sides, where the model in terms of the new parameter is the following:

Maximize Z() (3  2)x1  (5  )x2  (2  )x3, subject to

2x1  2x2  x3 5  6

3x1  x2  x3 10  8

and x1  0, x2  0, x3  0.

Construct the resulting revised final tableau (as a function of ), and convert this tableau to proper form from Gaussian elimination.

Use this tableau to identify the current basic solution as a function of . For   0, give the range of values of  for which this solution is both feasible and optimal. What is the best choice of  within this range?